# Relative geometric invariant theory

### Alexander H.W. Schmitt

Freie Universität Berlin, Germany

## Abstract

Relative geometric invariant theory is an invariant theory for equivariant projective morphisms between algebraic varieties endowed with an action of a reductive linear algebraic group. We will give brief accounts of the basic results of relative geometric invariant theory and present alternative proofs for recent results obtained by Halle, Hulek, and Zhang on the variation of quotients in relative geometric invariant theory.

## Cite this article

Alexander H.W. Schmitt, Relative geometric invariant theory. Enseign. Math. 67 (2021), no. 3/4, pp. 301–330

DOI 10.4171/LEM/1010