Consistency conditions for dimer models
Rings and Algebras
2011-04-11 v1 Algebraic Geometry
Abstract
Dimer models are a combinatorial tool to describe certain algebras that appear as noncommutative crepant resolutions of toric Gorenstein singularities. Unfortunately, not every dimer model gives rise to a noncommutative crepant resolution. Several notions of consistency have been introduced to deal with this problem. In this paper we study the major different notions in detail and show that for dimer models on a torus they are all equivalent.
Cite
@article{arxiv.1104.1592,
title = {Consistency conditions for dimer models},
author = {Raf Bocklandt},
journal= {arXiv preprint arXiv:1104.1592},
year = {2011}
}
Comments
This is an expanded version of the section on consistency in 'Calabi-Yau Algebras and Quiver Polyhedra' arXiv:0905.0232