Localization in quiver moduli spaces

TL;DR

This paper studies the structure of torus fixed points in quiver moduli spaces, describing their relation to stable representations of covering quivers and providing methods to construct and analyze these points.

Contribution

It introduces a new approach to describe torus fixed points via stable representations of covering quivers and develops a glueing method to construct a broad class of such quivers.

Findings

Lower bound for the Euler characteristic of quiver moduli spaces

Construction of all torus fixed points for certain roots

Description of fixed points via stable bipartite quivers

Abstract

Torus fixed points of quiver moduli spaces are given by stable representations of the universal (abelian) covering quiver. As far as the Kronecker quiver is concerned they can be described by stable representations of certain bipartite quivers coming along with a stable colouring. By use of the glueing method it is possible to construct a huge class of such quivers implying a lower bound for the Euler characteristic. For certain roots it is even possible to construct all torus fixed points.