The classification of special Cohen–Macaulay modules View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2010-05

AUTHORS

Osamu Iyama, Michael Wemyss

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. More... »

PAGES

41-83

References to SciGraph publications

  • 1988-12. Reflexive modules on quotient surface singularities in MATHEMATISCHE ANNALEN
  • 1980. Auslander-Reiten sequences and representation-finite algebras in REPRESENTATION THEORY I
  • 2005-08. τ-Categories I: Ladders in ALGEBRAS AND REPRESENTATION THEORY
  • 2005-10. τ-Categories II: Nakayama Pairs and Rejective Subcategories in ALGEBRAS AND REPRESENTATION THEORY
  • 1968-10. Rationale Singularitäten komplexer Flächen in INVENTIONES MATHEMATICAE
  • 1985-03. Reflexive modules over rational double points in MATHEMATISCHE ANNALEN
  • 1977-02. Die Invarianten der endlichen Untergruppen vonGL (2, ℂ) in MATHEMATISCHE ZEITSCHRIFT
  • 1987. Reflexive modules on cyclic quotient surface singularities in SINGULARITIES, REPRESENTATION OF ALGEBRAS, AND VECTOR BUNDLES
  • Journal

    TITLE

    Mathematische Zeitschrift

    ISSUE

    1

    VOLUME

    265

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00209-009-0501-3

    DOI

    http://dx.doi.org/10.1007/s00209-009-0501-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1029540868


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