Let X be a quotient surface singularity, and define 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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-3,
author = {Trond St\o len Gustavsen and Runar Ile},
title = {The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {41-50},
zbl = {1246.14008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-3}
}
Trond Stølen Gustavsen; Runar Ile. The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity. Banach Center Publications, Tome 95 (2011) pp. 41-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-3/