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• # Artykuł - szczegóły

## Banach Center Publications

2011 | 93 | 1 | 41-50

## The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity

EN

### Abstrakty

EN
Let X be a quotient surface singularity, and define $G^{def}(X,r)$ as the directed graph of maximal Cohen-Macaulay (MCM) modules with edges corresponding to deformation incidences. We conjecture that the number of connected components of $G^{def}(X,r)$ is equal to the order of the divisor class group of X, and when X is a rational double point (RDP), we observe that this follows from a result of A. Ishii. We view this as an enrichment of the McKay correspondence. For a general quotient singularity X, we prove the conjecture under an additional cancellation assumption. We discuss the deformation relation in some examples, and in particular we give all deformations of an indecomposable MCM module on a rational double point.

41-50

wydano
2011

### Twórcy

• Department of Education, Buskerud University College, P.O. Box 7053, N-3007 Drammen, Norway
autor
• Deparment of Mathematics, University of Bergen, P.O. Box 7803, N-5020 Bergen, Norway