Maximal Cohen-macaulay Modules over Non-isolated Surface Singularities and Matrix Problems

Ebook Details

Authors

Igor Burban, Yuriy Drozd

Year 2017
Pages 114
Publisher Amer Mathematical Society
Language en
ISBN 9781470425371
File Size 999.61 KB
File Format PDF
Download Counter 109
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Ebook Description

In this article the authors develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen-Macaulay representation type. The authors' approach is illustrated on the case of $\mathbb{k}[[ x,y,z]]/(xyz)$ as well as several other rings. This study of maximal Cohen-Macaulay modules over non-isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.