Non-commutative Crepant Resolutions

Abstract

We introduce the notion of a “non-commutative crepant” resolution of a singularity and show that it exists in certain cases. We also give some evidence for an extension of a conjecture by Bondal and Orlov, stating that different crepant resolutions of a Gorenstein singularity have the same derived category.KeywordsRational SingularityCoherent SheaveAmple Line BundleCoherent SheafTriangulate CategoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.