# Chevalley’s theorem

### Chevalley’s Theorem on constructible images made constructive

###### Talk at the workshop

Computational and algorithmic methods

The Isaac Newton Institute

Cambridge, United Kingdom

27 January 2020 to 31 January 2020

###### Abstract:

Chevalley proved that the image of an algebraic morphism between algebraic varieties is a constructible set. Examples are orbits of algebraic group actions. A constructible set in a topological space is a finite union of locally closed sets and a locally closed set is the difference of two closed subsets. Simple examples show that even if the source and target of the morphism are affine varieties the image may neither be affine nor quasi-affine. In this talk, I will present a Gröbner-basis-based algorithm that computes the constructible image of a morphism of affine spaces, along with some applications.