Oberwolfach Seminar: Cohen-Macaulay modules, Surface Singularities and McKay Correspondence

November 20th - November 26th, 2011
Igor Burban, Bonn
Yuriy Drozd, Kiev
Gert-Martin Greuel, Kaiserslautern

The study of maximal Cohen-Macaulay modules over Noetherian local rings has its origin in the theory of integral representations of finite groups. It grew up from a very classical problem of classification of crystallographic groups, related with Hilbert's 18-th problem. One of the most spectacular applications of the theory of Cohen-Macaulay modules is a conceptual explanation of the so-called McKay correspondence for finite subgroups of SL(2, C), due to Artin, Auslander, Esnault, Gonzalez-Sprinberg, Knörrer, Verdier and many others. A detailed discussion of these results is going to be one of the central aims of this school.

We are going to focus on the following subjects.

  1. Cohen-Macaulay modules over surface singularities and the McKay correspondence for the quotient surface singularities.
  2. Vector bundles on genus one curves, Kahn's functor and the geometric McKay correspondence for the minimally elliptic surface singularities.
  3. Cohen-Macaulay modules over degenerate cusps.
  4. Geometry of normal surface singularities.

Preparatory reading

References on vector bundles on genus one curves and Cohen-Macaulay modules over minimally elliptic singularities and their degenerations

Deadline for applications
15 September 2011

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 25. The Institute covers accommodation and food. We are pleased that the Carl Friedrich von Siemens Foundation has decided to support the Oberwolfach Seminars from summer 2008 to summer 2013. By this support, travel expenses can be reimbursed up to 200 Euro in average per person. Participants can ask for travel support during their stay in Oberwolfach at the guest office against copy of travel receipts. Applications including

should be sent preferably by e-mail (.ps or .pdf file) to:

    Prof. Dr. Dr. h.c. Gert-Martin Greuel
    Universität Kaiserslautern
    Fachbereich Mathematik
    Erwin Schrödingerstr.
    67663 Kaiserslautern, Germany

Mathematisches Forschungsinstitut Oberwolfach   updated: April 20 th, 2011