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Math401Math 401, Fall 2025: Thesis notesMath 401, Fall 2025: Thesis notes, S6, Algebraic Geometry

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

Affine algebraic variety

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

V=V({Fi}i∈I)={z∈Cn∣Fi(z)=0 for all i∈I}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 II may not be countable or finite.

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