Moduli spaces of slope-semistable pure sheaves

TL;DR

This paper constructs a moduli space for slope-semistable pure sheaves, extending existing frameworks and providing a compactification of the Simpson moduli space, along with an effective restriction theorem.

Contribution

It introduces a new moduli space for slope-semistable pure sheaves and offers a compactification of the Simpson moduli space of slope-stable reflexive sheaves.

Findings

Constructed a moduli space of slope-semistable pure sheaves.

Provided a compactification of the Simpson moduli space.

Proved an effective restriction theorem for slope-(semi)stable pure sheaves.

Abstract

We construct a moduli space of slope-semistable pure sheaves, building upon previous work of Le Potier and Jun Li on torsion-free sheaves over smooth surfaces. In particular, our construction provides a compactification of the Simpson moduli space of slope-stable reflexive sheaves. We also prove an effective restriction theorem for slope-(semi)stable pure sheaves following an approach due to Langer.