The classification of special Cohen–Macaulay modules

Iyama, O. and Wemyss, M. (2010) The classification of special Cohen–Macaulay modules. Mathematische Zeitschrift, 265(1), pp. 41-83. (doi:10.1007/s00209-009-0501-3)

[img]
Preview
Text
130849.pdf - Accepted Version

734kB

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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Wemyss, Professor Michael
Authors: Iyama, O., and Wemyss, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematische Zeitschrift
Publisher:Springer-Verlag
ISSN:0025-5874
ISSN (Online):1432-1823
Published Online:15 April 2009
Copyright Holders:Copyright © 2009 Springer-Verlag
First Published:First published in Mathematische Zeitschrift 265(1):41-83
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

University Staff: Request a correction | Enlighten Editors: Update this record