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

• Autorzy: Trond Stølen Gustavsen , Runar Ile
• Języki publikacji: 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.

Kategorie tematyczne

• 13C14: Cohen-Macaulay modules
• 14J17: Singularities
• 14B12: Local deformation theory, Artin approximation, etc.
• 14D20: Algebraic moduli problems, moduli of vector bundles

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 93
• Numer: 1
• Strony: 41-50

Daty

wydano

2011

Twórcy

autor

Trond Stølen Gustavsen

• Department of Education, Buskerud University College, P.O. Box 7053, N-3007 Drammen, Norway

autor

Runar Ile

• Deparment of Mathematics, University of Bergen, P.O. Box 7803, N-5020 Bergen, Norway

Identyfikatory

DOI

10.4064/bc93-0-3