Generating toric noncommutative crepant resolutions
Algebraic Geometry
2015-03-19 v1 Rings and Algebras
Abstract
We present an algorithm that finds all toric noncommutative crepant resolutions of a given toric 3-dimensional Gorenstein singularity. The algorithm embeds the quivers of these algebras inside a real 3-dimensional torus such that the relations are homotopy relations. One can project these embedded quivers down to a 2-dimensional torus to obtain the corresponding dimer models. We discuss some examples and use the algorithm to show that all toric noncommutative crepant resolutions of a finite quotient of the conifold singularity can be obtained by mutating one basic dimer model. We also discuss how this algorithm might be extended to higher dimensional singularities.
Cite
@article{arxiv.1104.1597,
title = {Generating toric noncommutative crepant resolutions},
author = {Raf Bocklandt},
journal= {arXiv preprint arXiv:1104.1597},
year = {2015}
}