Danilov resolution and representations of McKay quiver

TL;DR

This paper constructs McKay quiver representations on the Danilov resolution of certain singularities, showing it as the normalization of a moduli space component, and explicitly describes the stability conditions involved.

Contribution

It introduces a new family of McKay quiver representations on Danilov resolutions and characterizes the stability conditions explicitly for coprime parameters.

Findings

Resolution is the normalization of the moduli space component.

Explicit description of stability chambers for all coprime r, a.

Connects McKay quiver representations with geometric resolutions.

Abstract

We construct a family of McKay quiver representations on the Danilov resolution of the 1/r(1,a,r - a) singularity. It follows that the resolution is the normalization of the coherent component of the moduli space of stable McKay quiver representations for a suitable stability condition. We describe explicitly the corresponding chamber of stability conditions for any coprime numbers r, a.