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Algebraic geometry
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491
Table of contents
491
1. Algebraic curves
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Algebraic geometry
128
1.1. Cubic curves
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Algebraic curves
9
1.1.1. Cissoid of Diocles
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Cubic curves
1.1.2. Conchoid of de Sluze
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Cubic curves
1.1.3. Cubic plane curve
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Cubic curves
1.1.4. Folium of Descartes
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Cubic curves
1.1.5. Semicubical parabola
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Cubic curves
1.1.6. Trident curve
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Cubic curves
1.1.7. Trisectrix of Maclaurin
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Cubic curves
1.1.8. Tschirnhausen cubic
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Cubic curves
1.1.9. Witch of Agnesi
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Cubic curves
1.2. Riemann surfaces
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Algebraic curves
26
1.2.1. Kleinian groups
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Riemann surfaces
1.2.2. Behnke–Stein theorem on Stein manifolds
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Riemann surfaces
1.2.3. Bolza surface
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Riemann surfaces
1.2.4. Cusp neighborhood
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Riemann surfaces
1.2.5. Differential forms on a Riemann surface
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Riemann surfaces
1.2.6. Fenchel–Nielsen coordinates
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Riemann surfaces
1.2.7. First Hurwitz triplet
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Riemann surfaces
1.2.8. Fuchsian group
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Riemann surfaces
1.2.9. Fuchsian model
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Riemann surfaces
1.2.10. Gauss–Bonnet theorem
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Riemann surfaces
1.2.11. Hurwitz quaternion order
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Riemann surfaces
1.2.12. Hurwitz surface
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Riemann surfaces
1.2.13. Indigenous bundle
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Riemann surfaces
1.2.14. Macbeath surface
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Riemann surfaces
1.2.15. Mumford's compactness theorem
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Riemann surfaces
1.2.16. Poincaré metric
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Riemann surfaces
1.2.17. Prime form
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Riemann surfaces
1.2.18. Prym differential
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Riemann surfaces
1.2.19. Quillen determinant line bundle
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Riemann surfaces
1.2.20. Riemann surface
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Riemann surfaces
1.2.21. Schwarz–Ahlfors–Pick theorem
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Riemann surfaces
1.2.22. Simultaneous uniformization theorem
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Riemann surfaces
1.2.23. Spectral network
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Riemann surfaces
1.2.24. Uniformization theorem
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Riemann surfaces
1.2.25. Universal Teichmüller space
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Riemann surfaces
1.2.26. Weil–Petersson metric
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Riemann surfaces
1.3. Sextic curves
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Algebraic curves
10
1.3.1. Astroid
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Sextic curves
1.3.2. Atriphtaloid
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Sextic curves
1.3.3. Butterfly curve (algebraic)
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Sextic curves
1.3.4. Cayley's sextic
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Sextic curves
1.3.5. Coble curve
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Sextic curves
1.3.6. Nephroid
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Sextic curves
1.3.7. Quadrifolium
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Sextic curves
1.3.8. Watt's curve
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Sextic curves
1.3.9. Wiman's sextic
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Sextic curves
1.3.10. Wirtinger sextic
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Sextic curves
1.4. Toric sections
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Algebraic curves
2
1.4.1. Spiric sections
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Toric sections
1.4.2. Villarceau circles
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Toric sections
1.5. Abelian integral
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Algebraic curves
1.6. Abelian variety
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Algebraic curves
1.7. Abel–Jacobi map
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Algebraic curves
1.8. Acnode
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Algebraic curves
1.9. Algebraic curve
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Algebraic curves
1.10. Algebraic geometry code
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Algebraic curves
1.11. Artin–Schreier curve
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Algebraic curves
1.12. Belyi's theorem
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Algebraic curves
1.13. Bicorn
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Algebraic curves
1.14. Bifolium
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Algebraic curves
1.15. Bitangents of a quartic
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Algebraic curves
1.16. Brill–Noether theory
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Algebraic curves
1.17. Bring's curve
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Algebraic curves
1.18. Bullet-nose curve
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Algebraic curves
1.19. Cartesian oval
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Algebraic curves
1.20. Cassini oval
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Algebraic curves
1.21. Castelnuovo curve
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Algebraic curves
1.22. Chasles–Cayley–Brill formula
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Algebraic curves
1.23. Chiral Potts curve
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Algebraic curves
1.24. Cissoid
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Algebraic curves
1.25. Classical modular curve
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Algebraic curves
1.26. Conchoid of Dürer
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Algebraic curves
1.27. Crunode
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Algebraic curves
1.28. Cusp (singularity)
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Algebraic curves
1.29. De Franchis theorem
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Algebraic curves
1.30. Deltoid curve
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Algebraic curves
1.31. Enriques–Babbage theorem
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Algebraic curves
1.32. Epicycloid
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Algebraic curves
1.33. Fermat curve
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Algebraic curves
1.34. Generalized conic
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Algebraic curves
1.35. Genus–degree formula
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Algebraic curves
1.36. Hilbert's twenty-first problem
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Algebraic curves
1.37. Hippopede
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Algebraic curves
1.38. Hodge bundle
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Algebraic curves
1.39. Hyperelliptic curve
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Algebraic curves
1.40. Imaginary hyperelliptic curve
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Algebraic curves
1.41. Jacobian variety
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Algebraic curves
1.42. Kappa curve
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Algebraic curves
1.43. Kempe's universality theorem
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Algebraic curves
1.44. Klein quartic
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Algebraic curves
1.45. Lambda g conjecture
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Algebraic curves
1.46. Lange's conjecture
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Algebraic curves
1.47. Lemniscate of Bernoulli
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Algebraic curves
1.48. Limaçon
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Algebraic curves
1.49. Limaçon trisectrix
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Algebraic curves
1.50. List of curves
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Algebraic curves
1.51. Lüroth quartic
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Algebraic curves
1.52. Modular curve
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Algebraic curves
1.53. Moment curve
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Algebraic curves
1.54. Mumford measure
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Algebraic curves
1.55. N-ellipse
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Algebraic curves
1.56. Nagata's conjecture on curves
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Algebraic curves
1.57. Normal degree
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Algebraic curves
1.58. Ordinary singularity
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Algebraic curves
1.59. Parabola
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Algebraic curves
1.60. Plücker formula
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Algebraic curves
1.61. Polar curve
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Algebraic curves
1.62. Polynomial lemniscate
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Algebraic curves
1.63. Prym variety
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Algebraic curves
1.64. Quartic plane curve
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Algebraic curves
1.65. Rational normal curve
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Algebraic curves
1.66. Real hyperelliptic curve
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Algebraic curves
1.67. Real plane curve
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Algebraic curves
1.68. Reiss relation
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Algebraic curves
1.69. S-equivalence
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Algebraic curves
1.70. Sectrix of Maclaurin
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Algebraic curves
1.71. Singular point of a curve
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Algebraic curves
1.72. Sinusoidal spiral
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Algebraic curves
1.73. Spiric section
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Algebraic curves
1.74. Stable curve
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Algebraic curves
1.75. Superelliptic curve
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Algebraic curves
1.76. Tacnode
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Algebraic curves
1.77. Twisted cubic
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Algebraic curves
1.78. Vector bundles on algebraic curves
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Algebraic curves
1.79. Weber's theorem (Algebraic curves)
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Algebraic curves
1.80. Weierstrass point
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Algebraic curves
1.81. Weil reciprocity law
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Algebraic curves
2. Algebraic varieties
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Algebraic geometry
44
2.1. 3-folds
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Algebraic varieties
10
2.1.1. 3-fold
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3-folds
2.1.2. Barth–Nieto quintic
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3-folds
2.1.3. Burkhardt quartic
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3-folds
2.1.4. Consani–Scholten quintic
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3-folds
2.1.5. Fermat quintic threefold
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3-folds
2.1.6. Igusa quartic
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3-folds
2.1.7. Klein cubic threefold
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3-folds
2.1.8. Koras–Russell cubic threefold
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3-folds
2.1.9. Quartic threefold
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3-folds
2.1.10. Segre cubic
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3-folds
2.2. Quadrics
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Algebraic varieties
8
2.2.1. Confocal conic sections
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Quadrics
2.2.2. Conical surface
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Quadrics
2.2.3. Hypercone
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Quadrics
2.2.4. Jacobi ellipsoid
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Quadrics
2.2.5. Maclaurin spheroid
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Quadrics
2.2.6. Phenotypic response surfaces
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Quadrics
2.2.7. Quadrics (company)
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Quadrics
2.2.8. Spheroid
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Quadrics
2.3. Algebraic manifold
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Algebraic varieties
2.4. Branched covering
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Algebraic varieties
2.5. Canonical bundle
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Algebraic varieties
2.6. Coble variety
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Algebraic varieties
2.7. Complete variety
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Algebraic varieties
2.8. Complex algebraic variety
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Algebraic varieties
2.9. Cubic threefold
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Algebraic varieties
2.10. Degree of an algebraic variety
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Algebraic varieties
2.11. Function field of an algebraic variety
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Algebraic varieties
2.12. Geometric genus
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Algebraic varieties
2.13. Homogeneous coordinate ring
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Algebraic varieties
2.14. Homogeneous variety
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Algebraic varieties
2.15. Horrocks–Mumford bundle
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Algebraic varieties
2.16. Krivine–Stengle Positivstellensatz
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Algebraic varieties
2.17. Line complex
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Algebraic varieties
2.18. Moduli of algebraic curves
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Algebraic varieties
2.19. Mordellic variety
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Algebraic varieties
2.20. Pseudo-canonical variety
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Algebraic varieties
2.21. Quasi-projective variety
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Algebraic varieties
2.22. Quintic threefold
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Algebraic varieties
2.23. Seshadri constant
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Algebraic varieties
2.24. Singular point of an algebraic variety
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Algebraic varieties
2.25. Veronese surface
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Algebraic varieties
2.26. Weil restriction
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Algebraic varieties
3. Birational geometry
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Algebraic geometry
8
3.1. Birational invariant
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Birational geometry
3.2. Blowing up
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Birational geometry
3.3. Elliptic surface
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Birational geometry
3.4. Enriques surface
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Birational geometry
3.5. Enriques–Kodaira classification
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Birational geometry
3.6. Iitaka dimension
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Birational geometry
3.7. Rational surface
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Birational geometry
3.8. Surface of general type
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Birational geometry
4. Moduli theory
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Algebraic geometry
6
4.1. Character variety
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Moduli theory
4.2. J-line
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Moduli theory
4.3. Moduli scheme
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Moduli theory
4.4. Moduli space
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Moduli theory
4.5. Stable map
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Moduli theory
4.6. Stacky curve
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Moduli theory
5. Real algebraic geometry
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Algebraic geometry
14
5.1. Gudkov's conjecture
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Real algebraic geometry
5.2. Harnack's curve theorem
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Real algebraic geometry
5.3. Hilbert's seventeenth problem
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Real algebraic geometry
5.4. Nash functions
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Real algebraic geometry
5.5. Non-Archimedean ordered field
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Real algebraic geometry
5.6. Polytope
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Real algebraic geometry
5.7. Positive polynomial
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Real algebraic geometry
5.8. Ragsdale conjecture
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Real algebraic geometry
5.9. Semialgebraic set
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Real algebraic geometry
5.10. Semialgebraic space
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Real algebraic geometry
5.11. Semidefinite programming
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Real algebraic geometry
5.12. Subanalytic set
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Real algebraic geometry
5.13. Sum-of-squares optimization
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Real algebraic geometry
5.14. Tarski–Seidenberg theorem
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Real algebraic geometry
6. Scheme theory
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Algebraic geometry
13
6.1. Chevalley scheme
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Scheme theory
6.2. Equivariant sheaf
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Scheme theory
6.3. Fiber product of schemes
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Scheme theory
6.4. Function field (scheme theory)
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Scheme theory
6.5. Geometrically (algebraic geometry)
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Scheme theory
6.6. Gluing schemes
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Scheme theory
6.7. Picard group
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Scheme theory
6.8. Proj construction
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Scheme theory
6.9. Quotient by an equivalence relation
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Scheme theory
6.10. Scheme (mathematics)
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Scheme theory
6.11. Smooth scheme
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Scheme theory
6.12. Séminaire de Géométrie Algébrique du Bois Marie
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Scheme theory
6.13. Éléments de géométrie algébrique
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Scheme theory
7. Structures on manifolds
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Algebraic geometry
43
7.1. Complex manifolds
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Structures on manifolds
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7.1.1. Bergman metric
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Complex manifolds
7.1.2. Bismut connection
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Complex manifolds
7.1.3. Bott residue formula
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Complex manifolds
7.1.4. CR manifold
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Complex manifolds
7.1.5. Calabi conjecture
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Complex manifolds
7.1.6. Calabi–Eckmann manifold
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Complex manifolds
7.1.7. Complex affine space
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Complex manifolds
7.1.8. Complex differential form
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Complex manifolds
7.1.9. Complex torus
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Complex manifolds
7.1.10. Constant scalar curvature Kähler metric
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Complex manifolds
7.1.11. Ddbar lemma
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Complex manifolds
7.1.12. Hitchin functional
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Complex manifolds
7.1.13. Holomorphic Lefschetz fixed-point formula
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Complex manifolds
7.1.14. Holomorphic vector bundle
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Complex manifolds
7.1.15. Hopf manifold
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Complex manifolds
7.1.16. Kähler quotient
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Complex manifolds
7.1.17. Lelong number
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Complex manifolds
7.1.18. Mutation (Jordan algebra)
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Complex manifolds
7.1.19. Nonabelian Hodge correspondence
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Complex manifolds
7.1.20. Period domain
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Complex manifolds
7.1.21. Positive current
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Complex manifolds
7.1.22. Quadratic differential
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Complex manifolds
7.1.23. Siegel domain
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Complex manifolds
7.1.24. Siu's semicontinuity theorem
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Complex manifolds
7.1.25. Stein manifold
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Complex manifolds
7.1.26. Twistor space
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Complex manifolds
7.2. Differential structures
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Structures on manifolds
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7.2.1. Differential structure
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Differential structures
7.2.2. Hilbert's fifth problem
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Differential structures
7.3. Clifford module bundle
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Structures on manifolds
7.4. Foliation
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Structures on manifolds
7.5. Fréchet manifold
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Structures on manifolds
7.6. Hermitian connection
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Structures on manifolds
7.7. Hypercomplex manifold
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Structures on manifolds
7.8. Kosmann lift
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Structures on manifolds
7.9. Linear complex structure
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Structures on manifolds
7.10. Lipschitz continuity
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Structures on manifolds
7.11. Poisson–Lie group
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Structures on manifolds
7.12. Quaternion-Kähler manifold
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Structures on manifolds
7.13. Real structure
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Structures on manifolds
7.14. Sasakian manifold
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Structures on manifolds
7.15. Solvmanifold
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Structures on manifolds
8. Tropical geometry
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Algebraic geometry
1
8.1. Introduction to Tropical Geometry
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Tropical geometry
9. Complex geometry
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Algebraic geometry
10. Nonlinear algebra
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Algebraic geometry
1
10.1. Alekseev–Gröbner formula
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Nonlinear algebra
11. Adequate equivalence relation
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Algebraic geometry
12. Adjunction formula
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Algebraic geometry
13. Affine Grassmannian
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Algebraic geometry
14. Affine variety
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Algebraic geometry
15. Algebraic Geometry (book)
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Algebraic geometry
16. Algebraic cycle
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Algebraic geometry
17. Algebraic space
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Algebraic geometry
18. Algebraic stack
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Algebraic geometry
19. Algebraic variety
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Algebraic geometry
20. Alternating algebra
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Algebraic geometry
21. Amoeba (mathematics)
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Algebraic geometry
22. Ample line bundle
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Algebraic geometry
23. Analytic space
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Algebraic geometry
24. Arakelov theory
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Algebraic geometry
25. Arithmetic and geometric Frobenius
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Algebraic geometry
26. Artin's criterion
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Algebraic geometry
27. Associative algebra
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Algebraic geometry
28. Beilinson regulator
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Algebraic geometry
29. Berkovich space
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Algebraic geometry
30. Bloch's formula
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Algebraic geometry
31. Bloch's higher Chow group
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Algebraic geometry
32. Bott–Samelson resolution
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Algebraic geometry
33. Bracket ring
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Algebraic geometry
34. Bundle of principal parts
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Algebraic geometry
35. Canonical ring
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Algebraic geometry
36. Canonical singularity
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Algebraic geometry
37. Cartan subgroup
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Algebraic geometry
38. Cartier isomorphism
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Algebraic geometry
39. Castelnuovo–Mumford regularity
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Algebraic geometry
40. Categorical quotient
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Algebraic geometry
41. Cayleyan
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Algebraic geometry
42. Chordal variety
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Algebraic geometry
43. Chow group of a stack
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Algebraic geometry
44. Chow variety
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Algebraic geometry
45. Complex analytic variety
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Algebraic geometry
46. Cone (algebraic geometry)
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Algebraic geometry
47. Cone of curves
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Algebraic geometry
48. Conic bundle
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Algebraic geometry
49. Conifold
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Algebraic geometry
50. Contraction morphism
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Algebraic geometry
51. Convexity (algebraic geometry)
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Algebraic geometry
52. Correspondence (algebraic geometry)
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Algebraic geometry
53. Cotangent sheaf
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Algebraic geometry
54. Cox ring
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Algebraic geometry
55. Cramer's paradox
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Algebraic geometry
56. Crepant resolution
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Algebraic geometry
57. Crystal (mathematics)
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Algebraic geometry
58. Decomposition theorem of Beilinson, Bernstein and Deligne
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Algebraic geometry
59. Degeneration (algebraic geometry)
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Algebraic geometry
60. Deligne–Mumford stack
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Algebraic geometry
61. Derived noncommutative algebraic geometry
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Algebraic geometry
62. Derived stack
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Algebraic geometry
63. Derived tensor product
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Algebraic geometry
64. Determinantal variety
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Algebraic geometry
65. Diagonal morphism (algebraic geometry)
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Algebraic geometry
66. Differential of the first kind
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Algebraic geometry
67. Dimension of a scheme
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Algebraic geometry
68. Discrepancy (algebraic geometry)
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Algebraic geometry
69. Distribution on a linear algebraic group
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Algebraic geometry
70. Divisorial scheme
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Algebraic geometry
71. Donaldson–Thomas theory
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Algebraic geometry
72. Drinfeld module
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Algebraic geometry
73. Du Bois singularity
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Algebraic geometry
74. Dualizing sheaf
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Algebraic geometry
75. Dwork family
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Algebraic geometry
76. Enumerative geometry
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Algebraic geometry
77. Equisingularity
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Algebraic geometry
78. Exceptional divisor
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Algebraic geometry
79. F-crystal
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Algebraic geometry
80. Faithfully flat descent
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Algebraic geometry
81. Fake projective space
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Algebraic geometry
82. Family of curves
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Algebraic geometry
83. Fano fibration
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Algebraic geometry
84. Fano variety
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Algebraic geometry
85. Field of definition
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Algebraic geometry
86. Field with one element
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Algebraic geometry
87. Flag bundle
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Algebraic geometry
88. Flip (mathematics)
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Algebraic geometry
89. Fondements de la Géometrie Algébrique
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Algebraic geometry
90. Formal holomorphic function
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Algebraic geometry
91. Formal scheme
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Algebraic geometry
92. Foundations of Algebraic Geometry
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Algebraic geometry
93. Fourier–Deligne transform
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94. Frobenius manifold
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95. Frobenius splitting
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96. Fujiki class C
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97. Functor represented by a scheme
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98. GIT quotient
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99. GKM variety
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100. Gauss–Manin connection
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101. General elephant
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102. General position
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103. Generic property
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104. Geometric class field theory
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105. Geometric quotient
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106. Gibbons–Hawking space
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107. Glossary of algebraic geometry
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108. Glossary of arithmetic and diophantine geometry
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109. Gordan's lemma
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110. Gorenstein scheme
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111. Grassmann bundle
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112. Griffiths group
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113. Gromov–Witten invariant
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114. Grothendieck connection
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115. Group-scheme action
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116. Group-stack
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117. Group functor
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118. H topology
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119. Hilbert's arithmetic of ends
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120. Hironaka's example
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121. Horrocks bundle
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122. Hurwitz scheme
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123. Hyperplane section
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124. Hypersurface
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125. Hypertoric variety
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126. Imaginary line (mathematics)
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127. Ind-scheme
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128. Intersection number
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129. K-groups of a field
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130. K-stability of Fano varieties
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131. Kleiman's theorem
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132. Kobayashi metric
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133. Kodaira–Spencer map
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134. Kuga fiber variety
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135. Kähler manifold
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136. Level structure (algebraic geometry)
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137. List of algebraic geometry topics
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138. List of topologies on the category of schemes
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139. Local invariant cycle theorem
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140. Local uniformization
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141. Localized Chern class
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142. Log structure
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143. Logarithmic pair
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144. Main theorem of elimination theory
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145. Matsusaka's big theorem
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146. Max Noether's theorem on curves
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147. Milnor number
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148. Minimal model program
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149. Moduli stack of elliptic curves
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150. Moduli stack of principal bundles
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151. Moduli stack of vector bundles
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152. Morphism of algebraic stacks
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153. Morphism of schemes
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154. Motivic integration
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155. Multiplicative distance
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156. Nash blowing-up
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157. Newton–Okounkov body
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158. Nilcurve
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159. Nisnevich topology
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160. Noetherian scheme
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161. Noncommutative algebraic geometry
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162. Normal cone
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163. Normal crossing singularity
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164. Normal scheme
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165. Normally flat ring
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166. Numerical certification
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167. Néron–Severi group
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168. P-curvature
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169. Parshin's conjecture
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170. Period (algebraic geometry)
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171. Picard–Lefschetz theory
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172. Positive form
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173. Prestack
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174. Pseudoholomorphic curve
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175. Purity (algebraic geometry)
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176. Pursuing Stacks
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177. Quasi-separated morphism
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178. Quippian
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179. Quot scheme
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180. Quotient space of an algebraic stack
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181. Quotient stack
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182. Rational mapping
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183. Rational normal scroll
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184. Regular scheme
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185. Relative cycle
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186. Relative effective Cartier divisor
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187. Residue field
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188. Riemann–Roch-type theorem
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189. Ruled join
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190. Ruled variety
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191. Scheme-theoretic intersection
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192. Schubert calculus
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193. Scorza variety
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194. Secant variety
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195. Semistable reduction theorem
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196. Severi variety (Hilbert scheme)
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197. Siegel modular variety
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198. Smooth completion
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199. Smooth topology
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200. Spherical variety
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201. Stability (algebraic geometry)
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202. Stable vector bundle
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203. Standard monomial theory
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204. Stein factorization
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205. Steiner's conic problem
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206. Steinerian
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207. Sum of residues formula
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208. Supersingular variety
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209. Suslin homology
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210. Symmetric variety
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211. Syntomic topology
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212. Tangent space to a functor
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213. Tango bundle
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214. Tate topology
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215. Tate vector space
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216. Tautological ring
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217. Theorem of absolute purity
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218. Toric stack
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219. Toric variety
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220. Toroidal embedding
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221. Torsor (algebraic geometry)
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222. Trivial cylinder
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223. Trope (mathematics)
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224. V-topology
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225. Valuative criterion
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226. Wall-crossing
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227. Weighted projective space
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228. Witten conjecture
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229. Zariski space
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230. Zariski–Riemann space
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231. Étale spectrum
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232. Étale topology
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233. ℓ-adic sheaf
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Ancestors
Fields of mathematics
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