Consistency conditions for dimer models

Details Consistency conditions for dimer models Consistency conditions for dimer models

2011-04-08

arxiv.org/abs/1104.1592v1

Mathematics

Rings and Algebras

This is an expanded version of the section on consistency in 'Calabi-Yau Algebras and Quiver Polyhedra' arXiv:0905.0232

Scientific paper

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.

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