On two examples by Iyama and Yoshino

TL;DR

This paper explores two examples of isolated singularities, providing new approaches that connect them to cluster categories and Orlov's graded singularity category, leading to novel insights into their structure.

Contribution

It introduces two innovative methods to analyze isolated singularities, linking them to cluster categories and Orlov's theory, expanding understanding of their singularity categories.

Findings

Established a relation between examples and cluster categories.

Applied Orlov's results to obtain new insights into singularity categories.

Enhanced classification of Cohen-Macaulay modules over isolated singularities.

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.