On moduli spaces of quiver representations associated with dimer models

TL;DR

This paper establishes conditions under which the moduli space of quiver representations linked to dimer models is smooth and demonstrates that it provides a crepant resolution of a specific toric variety, connecting algebraic and geometric structures.

Contribution

It offers a sufficient condition for smoothness of the moduli space and proves it acts as a crepant resolution of the associated toric variety.

Findings

Moduli space is smooth under certain conditions.

The moduli space provides a crepant resolution.

Connection between quiver representations and toric geometry.

Abstract

We give a sufficient condition for the moduli space of quiver representations associated with a dimer model to be smooth for a general stability parameter. We also show that the moduli space in this case is a crepant resolution of the toric variety determined by the Newton polygon of the characteristic polynomial.