Slope-semistability and moduli of coherent sheaves: a survey

TL;DR

This survey reviews classical and recent results on the existence and construction of moduli spaces for semistable coherent sheaves in both algebraic and complex geometry contexts.

Contribution

It compiles and discusses known and new results on moduli space existence for semistable coherent sheaves across different geometric settings.

Findings

Comprehensive overview of moduli space constructions

Comparison of algebraic and complex geometric approaches

Identification of open problems in the field

Abstract

We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.