Localization in quiver moduli

TL;DR

This paper describes the fixed point set under a torus action on moduli spaces of quiver representations and uses this to compute their Euler characteristic, advancing understanding of their geometric structure.

Contribution

It provides a detailed description of fixed points in quiver moduli under torus actions and introduces a method to compute their Euler characteristics.

Findings

Fixed point set characterized under torus action

Euler characteristic of quiver moduli computed

Enhanced understanding of moduli space geometry

Abstract

The fixed point set under a natural torus action on projectivized moduli spaces of simple representations of quivers is described. As an application, the Euler characteristic of these moduli is computed.