Complex algebraic variety

A **complex algebraic variety** is a fundamental concept in algebraic geometry, which is the study of geometric objects defined by polynomial equations. Specifically, a complex algebraic variety is defined over the field of complex numbers \(\mathbb{C}\). ### Definitions: 1. **Algebraic Variety**: An algebraic variety is a set of solutions to one or more polynomial equations. The most common setting is within affine or projective space.