Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
July 2017
|
| Series: | Memoirs of the American Mathematical Society
1178 |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references |
| Physical Description: | xiv, 114, 4 ungezählte Seiten |
| ISBN: | 9781470425371 |
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MARC
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| 245 | 1 | 0 | |a Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems |c Igor Burban, Yuriy Drozd |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c July 2017 | |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 248, number 1178 (fourth of 5 numbers) | |
| 500 | |a Includes bibliographical references | ||
| 700 | 1 | |a Drozd, Jurij Anatolijovyč |d 1944- |0 (DE-588)1089201230 |4 aut | |
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Record in the Search Index
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| adam_text | Contents
Introduction, motivation and historical remarks ix
Chapter 1. Generalities on maximal Cohen-Macaulay modules 1
1.1. Maximal Cohen-Macaulay modules over surface singularities 1
1.2. On the category CM!f(A) 3
Chapter 2. Category of triples in dimension one 5
Chapter 3. Main construction 11
Chapter 4. Serre quotients and proof of Main Theorem 17
Chapter 5. Singularities obtained by gluing cyclic quotient singularities 27
5.1. Non-isolated surface singularities obtained by gluing normal rings 27
5.2. Generalities about cyclic quotient singularities 30
5.3. Degenerate cusps and their basic properties 31
5.4. Irreducible degenerate cusps 32
5.5. Other cases of degenerate cusps which are complete intersections 33
Chapter 6. Maximal Cohen-Macaulay modules over kfx, y, z /(x2 4- y3 — xyz) 35
Chapter 7. Representations of decorated bunches of chains-I 41
7.1. Notation 41
7.2. Bimodule problems 41
7.3. Definition of a decorated bunch of chains 46
7.4. Matrix description of the category Rep(X) 47
7.5. Strings and Bands 49
7.6. Idea of the proof 53
7.7. Decorated Kronecker problem 55
Chapter 8. Maximal Cohen-Macaulay modules over degenerate cusps-I 59
8.1. Maximal Cohen-Macaulay modules on cyclic quotient surface
singularities 59
8.2. Matrix problem for degenerate cusps 62
8.3. Reconstruction procedure 64
8.4. Cohen-Macaulay representation type and tameness of degenerate
cusps 66
Chapter 9. Maximal Cohen-Macaulay modules over degenerate cusps-II 71
9.1. Maximal Cohen-Macaulay modules over k[x, y, z /(xyz) 71
9.2. Maximal Cohen-Macaulay modules over y, uf v /(xy, uv) 76
9.3. Degenerate cusp 3k Jar, y, 2, w, v f(xz, xu, yu, yu, zv) 78
v
VI
CONTENTS
Chapter 10. Schreyer’s question 79
Chapter 11. Remarks on rings of discrete and tame CM-representation type 83
11.1. Non-reduced curve singularities 83
11.2. Maximal Cohen-Macaulay modules over the ring D((1,0)) 83
11.3. Other surface singularities of discrete and tame CM-representation
type 85
11.4. On deformations of certain non-isolated surface singularities 86
Chapter 12. Representations of decorated bunches of chains-II 89
12.1. Decorated conjugation problem 89
12.2. Some preparatory results from linear algebra 91
12.3. Reduction to the decorated chessboard problem 92
12.4. Reduction procedure for the decorated chessboard problem 94
12.5. Indecomposable representations of a decorated chessboard 98
12.6. Proof of the Classification Theorem 101
References 111
|
| any_adam_object | 1 |
| author | Burban, Igor 1977- Drozd, Jurij Anatolijovyč 1944- |
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| author_facet | Burban, Igor 1977- Drozd, Jurij Anatolijovyč 1944- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 130 SK 240 |
| ctrlnum | (OCoLC)981907996 (DE-599)GBV884461181 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV044449033 |
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| indexdate | 2024-07-10T07:53:15Z |
| institution | BVB |
| isbn | 9781470425371 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029850004 |
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| physical | xiv, 114, 4 ungezählte Seiten |
| publishDate | 2017 |
| publishDateSearch | 2017 |
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| publisher | American Mathematical Society |
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| series2 | Memoirs of the American Mathematical Society |
| spelling | Burban, Igor 1977- (DE-588)125003897 aut Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems Igor Burban, Yuriy Drozd Providence, Rhode Island American Mathematical Society July 2017 xiv, 114, 4 ungezählte Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 248, number 1178 (fourth of 5 numbers) Includes bibliographical references Drozd, Jurij Anatolijovyč 1944- (DE-588)1089201230 aut Memoirs of the American Mathematical Society 1178 (DE-604)BV008000141 1178 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029850004&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burban, Igor 1977- Drozd, Jurij Anatolijovyč 1944- Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems Memoirs of the American Mathematical Society |
| title | Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems |
| title_auth | Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems |
| title_exact_search | Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems |
| title_full | Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems Igor Burban, Yuriy Drozd |
| title_fullStr | Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems Igor Burban, Yuriy Drozd |
| title_full_unstemmed | Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems Igor Burban, Yuriy Drozd |
| title_short | Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems |
| title_sort | maximal cohen macaulay modules over non isolated surface singularities and matrix problems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029850004&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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