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Generating Toric Noncommutative Crepant Resolutions

Lookup NU author(s): Dr Rafael Bocklandt

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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.

Publication metadata

Author(s): Bocklandt R

Publication type: Article

Publication status: Published

Journal: Journal of Algebra

Year: 2012

Volume: 364

Pages: 119-147

Print publication date: 23/04/2012

ISSN (print): 0021-8693

ISSN (electronic): 1090-266X

Publisher: Academic Press

URL: http://dx.doi.org/10.1016/j.jalgebra.2012.03.040

DOI: 10.1016/j.jalgebra.2012.03.040

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