On two examples by Iyama and Yoshino

Abstract

In the recent paper "Mutation in triangulated categories and rigid Cohen-Macaulay modules" Iyama and Yoshino consider 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. We obtain some new results on the singularity category of isolated singularities which may be interesting in their own right.

The first name of the first author was misspelled in the arXiv abstract. There are no changes in the paper

References in corpus (2)

• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Acyclic Calabi-Yau categories

Cited by in corpus (11)

• Adjunctions and defects in Landau-Ginzburg models
• Orlov spectra: bounds and gaps
• A categorification of Grassmannian cluster algebras
• Surfaces of minimal degree of tame representation type and mutations of Cohen-Macaulay modules
• Matrix factorizations via Koszul duality
• Reconstruction from Koszul homology and applications to module and derived categories
• Annihilators and dimensions of the singularity category
• Descent conditions for generation in derived categories
• High Frobenius pushforwards generate the bounded derived category
• Equivalences of stable categories of Gorenstein local rings
• Singularity categories via higher McKay quivers with potential