affine variety
/ˈæf.faɪn ˈveə.rɪ.ti/ · af·fine var·i·e·ty
noun
- In algebraic geometry, an affine variety is an irreducible subset of affine n‑space over an algebraically closed field that can be described as the common zero set of a collection of polynomial functions. The set of points (x, y) in ℂ² satisfying y = x³ is an affine variety because it is the zero locus of the polynomial y − x³ and is irreducible.
Synonyms
affine algebraic setirreducible affine algebraic setaffine algebraic varietyzero locusalgebraic set in affine space
Antonyms
Did you know? The modern definition of an affine variety was solidified by David Hilbert's basis theorem, which linked the geometry of these varieties to the algebraic properties of polynomial ideals.