Fixed point locus of Moduli spaces of Sheaves on Toric DM stacks

TL;DR

This paper develops a combinatorial framework for analyzing torsion free sheaves on smooth toric DM stacks, explicitly describing fixed point loci to facilitate computation of topological invariants.

Contribution

It extends existing combinatorial descriptions to higher dimensions and explicitly characterizes fixed point loci of moduli spaces on toric DM stacks.

Findings

Explicit description of fixed point loci in terms of characteristic functions

Extension of combinatorial methods to higher-dimensional toric DM stacks

Framework for computing topological invariants of moduli spaces

Abstract

Extending work of Klyachko, Perling and Kool we develop a combinatorial description of torsion free toric sheaves in any dimension on smooth toric DM stacks. We investigate their basic properties and under certain conditions recover some known results on smooth toric varieties. The action of the torus lifts to the moduli of torsion free modified Gieseker stable sheaves on the smooth DM stack, and we express its fixed point locus explicitly in terms of certain finer invariants called characteristic functions. These techniques will be exploited to compute topological invariants of the moduli of modified stable torsion free sheaves on smooth toric DM stacks.