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

Trond Stølen Gustavsen, and Runar Ile. "The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity." Banach Center Publications 93.1 (2011): 41-50. <http://eudml.org/doc/286428>.

@article{TrondStølenGustavsen2011,
abstract = {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.},
author = {Trond Stølen Gustavsen, Runar Ile},
journal = {Banach Center Publications},
keywords = {quotient singularities; modules; deformation theory},
language = {eng},
number = {1},
pages = {41-50},
title = {The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity},
url = {http://eudml.org/doc/286428},
volume = {93},
year = {2011},
}

TY - JOUR
AU - Trond Stølen Gustavsen
AU - Runar Ile
TI - The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity
JO - Banach Center Publications
PY - 2011
VL - 93
IS - 1
SP - 41
EP - 50
AB - 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.
LA - eng
KW - quotient singularities; modules; deformation theory
UR - http://eudml.org/doc/286428
ER -