Desingularizations of Quiver Grassmannians for the Equioriented Cycle Quiver

TL;DR

This paper develops a method to resolve singularities in quiver Grassmannians associated with nilpotent representations of equioriented cycle quivers and uses this to compute their torus equivariant cohomology.

Contribution

It introduces a construction of torus equivariant desingularizations for quiver Grassmannians of arbitrary nilpotent representations in the equioriented cycle case.

Findings

Successful desingularization of quiver Grassmannians

Explicit computation of torus equivariant cohomology

Framework applicable to arbitrary nilpotent representations

Abstract

We construct torus equivariant desingularizations of quiver Grassmannians for arbitrary nilpotent representations of an equioriented cycle quiver. We apply this to the computation of their torus equivariant cohomology.