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On two examples by Iyama and Yoshino

Part of: Theory of modules and ideals Homological methods

Published online by Cambridge University Press:  09 February 2011

Bernhard Keller ,
Daniel Murfet  and
Michel Van den Bergh
Bernhard Keller
Affiliation:
UFR de Mathématiques, Université Denis Diderot – Paris 7, 2, place Jussieu, 75251 Paris Cedex 05, France (email: [email protected])
Daniel Murfet
Affiliation:
Hausdorff Center for Mathematics, Endenicher Allee 62, D-53115 Bonn, Germany (email: [email protected])
Michel Van den Bergh
Affiliation:
Departement WNI, Universiteit Hasselt, Universitaire Campus, Building D, 3590 Diepenbeek, Belgium (email: [email protected])
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Abstract

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In a recent paper, Iyama and Yoshino considered two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal Cohen–Macaulay modules in terms of linear algebra data. In this paper, we present two new approaches to these examples. In the first approach we give a relation with cluster categories. In the second approach we use Orlov’s result on the graded singularity category.

Keywords

singularity categorymaximal Cohen–Macaulay modules

MSC classification

Secondary: 13C14: Cohen-Macaulay modules 16E65: Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 2 , March 2011 , pp. 591 - 612
Copyright
Copyright © Foundation Compositio Mathematica 2011

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