Moduli Spaces of Coherent Sheaves on Projective Deligne-Mumford Stacks over Algebraic Spaces

TL;DR

This paper constructs and proves the projectivity of moduli spaces of semistable sheaves on projective Deligne-Mumford stacks over algebraic spaces, advancing the understanding of geometric invariant theory in this context.

Contribution

It introduces a method to construct moduli spaces of semistable sheaves on stacks over algebraic spaces and proves their projectivity.

Findings

Moduli spaces are projective over the base algebraic space.

Constructed moduli spaces of semistable sheaves on stacks.

Established geometric invariant theory on algebraic spaces.

Abstract

In this paper, we study the geometric invariant theory on algebraic spaces, and construct te moduli spaces of $\mathcal{H}$-semistable sheaves on projective Deligne-Mumford stacks over algebraic spaces $S$. We prove that this moduli space is projective over $S$ as an algebraic space.