Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems
by Burban, Igor
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…
Read More ↓Title Statements
- Full title :Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems / Igor Burban, Yuriy Drozd.
Summary
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 singulari.
Read More ↓Edition Statements
- Publication Date:©2017
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, Rhode Island
- Language:eng
- Publication Date:©2017
Notes
"Volume 248, number 1178 (fourth of 5 numbers), July 2017."
The Physical Object
- Description:1 online resource (xiv, 114 pages) : : illustrations
Edition Identifiers
- ISBN:9781470440589, 147044058X
- oclc:ocn993440488
- LC Classification:QA251.3
- Dewey Decimal:512/.44
Table of Contents
Cover; Title page; Introduction, motivation and historical remarks; Chapter 1. Generalities on maximal Cohen-Macaulay modules; 1.1. Maximal Cohen-Macaulay modules over surface singularities; 1.2. On the category \CM^{ }(\rA); Chapter 2. Category of triples in dimension one; Chapter 3. Main construction; Chapter 4. Serre quotients and proof of Main Theorem; Chapter 5. Singularities obtained by gluing cyclic quotient singularities; 5.1. Non-isolated surface singularities obtained by gluing normal rings; 5.2. Generalities about cyclic quotient singularities.
5.3. Degenerate cusps and their basic properties5.4. Irreducible degenerate cusps; 5.5. Other cases of degenerate cusps which are complete intersections; Chapter 6. Maximal Cohen-Macaulay modules over \kk\llbracket, \rrbracket/(²+ ³- ); Chapter 7. Representations of decorated bunches of chains-I; 7.1. Notation; 7.2. Bimodule problems; 7.3. Definition of a decorated bunch of chains; 7.4. Matrix description of the category \Rep(\dX); 7.5. Strings and Bands; 7.6. Idea of the proof; 7.7. Decorated Kronecker problem; Chapter 8. Maximal Cohen-Macaulay modules over degenerate cusps-I.
8.1. Maximal Cohen-Macaulay modules on cyclic quot…
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