Moduli of sheaves: a modern primer

TL;DR

This paper provides a modern overview of the theory of moduli of sheaves, including recent developments and a symmetric formulation using gerbes, bridging classical and contemporary perspectives.

Contribution

It introduces a symmetric approach to moduli of sheaves via gerbes, updating classical theory with recent results from the last decade.

Findings

Comprehensive review of classical moduli theory

Introduction of gerbes for a symmetric formulation

Compilation of recent advances in the field

Abstract

We give a modern introduction to the moduli of sheaves. After reviewing the classical theory, we give a catalogue of results from the last decade. We then consider a more "symmetric" formulation of the theory by working with gerbes from the start.