Non-commutative crepant resolutions
arXiv:math/0211064
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.
The main reason for this new version is that the argument for the existence of non-commutative crepant resolutions for cones of Del Pezzo surfaces was incorrect in the published version of this paper. Luckily the statement follows easily from the work of Kuleshov and Orlov. This approach was suggested to the author by Tom Bridgeland