Semi-steady non-commutative crepant resolutions via regular dimer models

Abstract

A consistent dimer model gives a non-commutative crepant resolution (= NCCR) of a 3dimensional Gorenstein toric singularity. In particular, it is known that a consistent dimer model gives a class of NCCRs called steady if and only if it is homotopy equivalent to a regular hexagonal dimer model. Inspired by this result, we detect another nice property on NCCRs that characterizes square dimer models. We call such NCCRs semi-steady NCCRs, and study their properties.