nLab
zero locus

Contents

Idea

The zero locus or vanishing locus of a function is the set of points where it is vanishes, in that it takes the value zero.

Definition

For f:X𝔸f \colon X \to \mathbb{A} a function, its zero locus is the preimage f 1(0)f^{-1}(0) of zero, hence the level set at 0.

Properties

Nullstellensatz

Hilbert’s Nullstellensatz (German: “zero locus theorem”) characterizes joint zero loci of ideals of functions in a polynomial ring.

Last revised on December 8, 2017 at 04:56:08. See the history of this page for a list of all contributions to it.