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.
- Cohen-Macaulay modules over surface singularities and the McKay
correspondence for the quotient surface singularities.
Vector bundles on genus one curves, Kahn's functor and the geometric McKay correspondence
for the minimally elliptic surface singularities.
- Cohen-Macaulay modules over degenerate cusps.
Geometry of normal surface singularities.
- Preparatory reading
W. Bruns, J. Herzog, Cohen-Macaulay rings,
Cambridge Studies in Advanced Mathematics, 39. Cambridge University Press, Cambridge, 1993.
- I. Burban, Yu. Drozd, Maximal Cohen-Macaulay modules over surface singularities,
in Trends in representation theory of algebras and related topics, 101-166, 2008.
- J.-P. Serre, Local Algebra, Springer Monographs in Mathematics, 2000.
- Yu. Yoshino, Cohen-Macaulay modules over Cohen-Macaulay rings, LMS Lecture Note Series, 146. Cambridge University Press, Cambridge, 1990.
- References on vector bundles on genus one curves and Cohen-Macaulay modules over minimally elliptic singularities
and their degenerations
- L. Bodnarchuk, I. Burban, Yu. Drozd, G.-M. Greuel,
Vector bundles and torsion free sheaves on degenerations of elliptic curves,
Global aspects of complex geometry, 83-128, Springer, 2006.
- I. Burban, Yu. Drozd,
Maximal Cohen-Macaulay modules over non-isolated surface singularities,
- Yu. Drozd, Vector bundles and Cohen-Macaulay modules, in Representations of finite dimensional algebras and related topics in Lie theory and geometry, 189-222, Fields Inst. Communications
C. Kahn, Reflexive modules on minimally elliptic singularities,
Math. Ann. 285 (1989), no. 1, 141-160.
- 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.
- full name and address, including e-mail address
- present position, university
- name of supervisor of Ph.D. thesis
- a short summary of previous work and interest
should be sent preferably by e-mail (.ps or .pdf file) to:
Prof. Dr. Dr. h.c. Gert-Martin Greuel
Mathematisches Forschungsinstitut Oberwolfach
updated: April 20 th, 2011
67663 Kaiserslautern, Germany