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On two examples by Iyama and Yoshino. (English) Zbl 1264.13016
Summary: O. Iyama and Y. Yoshino [Invent. Math. 172, No. 1, 117–168 (2008; Zbl 1140.18007)] 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.

MSC:
13C14 Cohen-Macaulay modules
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
18E30 Derived categories, triangulated categories (MSC2010)
16G20 Representations of quivers and partially ordered sets
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