Moduli spaces of slope-semistable sheaves with reflexive Seshadri graduations

TL;DR

This paper investigates the structure of moduli stacks of slope-semistable sheaves with reflexive or locally free Seshadri graduations, establishing their openness and the existence of good moduli spaces, including quasi-projective schemes in the locally free case.

Contribution

It introduces the moduli stacks of such sheaves, proves their openness, and constructs their good moduli spaces, including quasi-projective schemes for locally free sheaves.

Findings

Moduli stacks are open in the stack of coherent sheaves.

Existence of good moduli spaces in characteristic zero.

Quasi-projective schemes for locally free sheaves.

Abstract

We study the moduli stacks of slope-semistable torsion-free coherent sheaves that admit reflexive, respectively locally free, Seshadri graduations on a smooth projective variety. We show that they are open in the stack of coherent sheaves and that they admit good moduli spaces when the field characteristic is zero. In addition, in the locally free case we prove that the resulting moduli space is a quasi-projective scheme.