Multiplicity-one theorem

The Multiplicity-One Theorem is a concept in the field of algebraic geometry, particularly in the study of algebraic varieties and their singularities. It is often applied in the context of intersections of algebraic varieties, particularly in relation to issues involving the dimension and the multiplicity of points of intersection. In general terms, the Multiplicity-One Theorem states that if two varieties intersect transversely at a point, then the intersection at that point has multiplicity one.