Videos

Non-commutative desingularizations and MCM modules I

Presenter
January 31, 2013
Keywords:
  • noncommutative algebraic geometry
  • D-modules
  • deformation quantization
  • derived categories
  • resolution of singularities
  • Cohen-Macaulay modules
  • McKay correspondence
  • Dynkin diagram classifications
MSC:
  • 13D09
  • 13D10
  • 13Dxx
  • 13-xx
  • 14Fxx
  • 14F05
  • 14F10
  • 14A22
  • 16E65
Abstract
I will describe some recent work on non-commutative analogs of resolutions of singularities, with a focus on the contribution made by maximal Cohen-Macaulay modules. This will include an overview of some approaches to non-commutative desingularizations in general, with specific attention to Van den Bergh's definition of a non-commutative crepant resolution. A key motivating example is Auslander's algebraic McKay correspondence between MCM modules over the Kleinian singularities, skew group rings of the binary polyhedral groups, and the affine ADE Coxeter-Dynkin diagrams.