The classification of special Cohen-Macaulay modules

Osamu Iyama, Michael Wemyss

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we completely classify all the special Cohen-Macaulay (=CM) modules corresponding to the exceptional curves in the dual graph of the minimal resolutions of all two dimensional quotient singularities. In every case we exhibit the specials explicitly in a combinatorial way. Our result relies on realizing the specials as those CM modules whose first Ext group vanishes against the ring R, thus reducing the problem to combinatorics on the AR quiver; such possible AR quivers were classified by Auslander and Reiten. We also give some general homological properties of the special CM modules and their corresponding reconstruction algebras.

Original languageEnglish
Pages (from-to)41-83
Number of pages43
JournalMathematische zeitschrift
Volume265
Issue number1
DOIs
Publication statusPublished - May 2010

Keywords

  • QUOTIENT SURFACE SINGULARITIES
  • REFLEXIVE MODULES
  • RATIONAL-SINGULARITIES
  • SUBCATEGORIES
  • DIMENSION

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