Singularity categories of deformations of Kleinian singularities

Simon Crawford (University of Edinburgh)

Wednesday 16th November, 2016 16:00-17:00 Maths 522


The Kleinian singularities make up a family of well-understood (commutative) surface singularities. In 1998, Crawley-Boevey and Holland introduced a family of algebras which may be viewed as noncommutative deformations of Kleinian singularities. Using singularity categories, I will make comparisons between the types of singularity arising in the commutative and noncommutative settings. I will also show that the "most singular" of these noncommutative deformations has a noncommutative resolution for which an analogue of the geometric McKay correspondence holds.

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