#
nLab
zero locus

Contents
# Contents

## Idea

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

## Definition

For $f \colon X \to \mathbb{A}$ a function, its *zero locus* is the preimage $f^{-1}(0)$ 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 June 24, 2022 at 16:39:39.
See the history of this page for a list of all contributions to it.