Lecture Notes on Quiver Representations and Moduli Problems in Algebraic Geometry

TL;DR

This paper provides an introduction to moduli spaces in algebraic geometry, focusing on quiver representations and their associated moduli spaces, including stable and semistable cases, quiver varieties, and related geometric objects.

Contribution

It offers a comprehensive overview of moduli space constructions for quiver representations, connecting classical and modern approaches in algebraic geometry.

Findings

Construction of moduli spaces for stable and semistable quiver representations

Description of Nakajima's quiver varieties

Introduction of quiver analogs of classical moduli spaces

Abstract

These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand the construction of the moduli spaces of stable and semistable quiver representations due to King, Nakajima's quiver varieties, as well as some 'quiver versions' of existing moduli spaces of algebra-geometric objects.