NoteNextra-origin/content/Math401/Extending_thesis/Math401_S6.md

Math 401, Fall 2025: Thesis notes, S6, Algebraic Geometry

Affine algebraic variety

The affine algebraic variety is the common zero set of a collection \{F_i\}_{i\in I} of complex polynomials on complex n-space \mathbb{C}^n. We write

V=\mathbb{V}(\{F_i\}_{i\in I})=\{z\in \mathbb{C}^n\vert F_i(z)=0\text{ for all } i\in I\}

Note that I may not be countable or finite.