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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 $f \colon X \to \mathbb{A}$ 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 December 8, 2017 at 04:56:08.
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