# Stratifying quotient stacks and moduli stacks

Berczi, G
Hoskins, V
Kirwan, F

24 November 2018

## Journal:

Abelsymposium 2017: Geometry of Moduli

## Last Updated:

2021-03-23T08:22:22.95+00:00

14

## DOI:

10.1007/978-3-319-94881-2_1

1-33

## abstract:

Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X∕H], where X is a projective scheme and H is a linear algebraic group with internally graded unipotent radical acting linearly on X, in such a way that each stratum [S∕H] has a geometric quotient S∕H. This leads to stratifications of moduli stacks (for example, sheaves over a projective scheme) such that each stratum has a coarse moduli space.

826669

Submitted

Conference Paper

9783319948812