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arXiv · 1104.1597

Generating toric noncommutative crepant resolutions

Raf 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.

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Raf Bocklandt. 2011-04-08. Generating toric noncommutative crepant resolutions. https://arxiv.org/abs/1104.1597

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