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)

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