| Description |
1 online resource (xiv, 114 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 248, number 1178 |
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Memoirs of the American Mathematical Society ; no. 1178.
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| 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 \CM̂{ }(\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 |
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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 |
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8.1. Maximal Cohen-Macaulay modules on cyclic quotient surface singularities8.2. Matrix problem for degenerate cusps; 8.3. Reconstruction procedure; 8.4. Cohen-Macaulay representation type and tameness of degenerate cusps; Chapter 9. Maximal Cohen-Macaulay modules over degenerate cusps-II; 9.1. Maximal Cohen-Macaulay modules over \kk\llbracket, \rrbracket/(); 9.2. Maximal Cohen-Macaulay modules over \kk\llbracket, \rrbracket/(,); 9.3. Degenerate cusp \kk\llbracket, \rrbracket/(,); Chapter 10. Schreyer's question |
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Chapter 11. Remarks on rings of discrete and tame CM-representation type11.1. Non-reduced curve singularities; 11.2. Maximal Cohen-Macaulay modules over the ring ̃ ((1,0)); 11.3. Other surface singularities of discrete and tame CM-representation type; 11.4. On deformations of certain non-isolated surface singularities; Chapter 12. Representations of decorated bunches of chains-II; 12.1. Decorated conjugation problem; 12.2. Some preparatory results from linear algebra; 12.3. Reduction to the decorated chessboard problem; 12.4. Reduction procedure for the decorated chessboard problem |
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12.5. Indecomposable representations of a decorated chessboard12.6. Proof of the Classification Theorem; References; Back Cover |
| 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 |
| Notes |
"Volume 248, number 1178 (fourth of 5 numbers), July 2017." |
| Bibliography |
Includes bibliographical references (pages 111-114) |
| Notes |
Print version record |
| Subject |
Cohen-Macaulay modules.
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Modules (Algebra)
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Singularities (Mathematics)
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Matrices.
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Cohen-Macaulay modules.
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Matrices.
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Modules (Algebra)
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Singularities (Mathematics)
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| Form |
Electronic book
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| Author |
Drozd, Yurij A., author.
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American Mathematical Society, publisher
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| LC no. |
2017014982 |
| ISBN |
9781470440589 |
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147044058X |
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