We study variations of tautological bundles on moduli spaces of representations of quivers with relations associated with dimer models under a change of stability parameters. We prove that if the tautological bundle induces a derived equivalence for some stability parameter, then the same holds for any generic stability parameter, and any projective crepant resolution can be obtained as the moduli space for some stability parameter. This result is used in [IU] to prove the abelian McKay correspondence without using the result of Bridgeland, King and Reid [BKR01].
"Dimer models and crepant resolutions." Hokkaido Math. J. 45 (1) 1 - 42, February 2016. https://doi.org/10.14492/hokmj/1470080746