Betti numbers of the moduli space of rank 3 parabolic Higgs bundles:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2007
|
| Series: | Memoirs of the American Mathematical Society
879 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "May 2007, volume 187, number 879 (end of volume)." Includes bibliographical references |
| Physical Description: | VII, 80 S. |
| ISBN: | 9780821839720 |
Staff View
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| 245 | 1 | 0 | |a Betti numbers of the moduli space of rank 3 parabolic Higgs bundles |c O. García-Prada ; P.B. Gathen ; V. Muñoz |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2007 | |
| 300 | |a VII, 80 S. | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 879 | |
| 500 | |a "May 2007, volume 187, number 879 (end of volume)." | ||
| 500 | |a Includes bibliographical references | ||
| 650 | 7 | |a Geometria algébrica |2 larpcal | |
| 650 | 7 | |a Moduli spaces |2 gtt | |
| 650 | 7 | |a Vectorbundels |2 gtt | |
| 650 | 4 | |a Vector bundles | |
| 650 | 4 | |a Moduli theory | |
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| 689 | 0 | 1 | |a Modultheorie |0 (DE-588)4170336-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Gothen, Peter B. |e Verfasser |4 aut | |
| 700 | 1 | |a Muñoz, Vicente |e Verfasser |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter 1. Introduction 1
Chapter 2. Parabolic Higgs bundles 5
1. Definitions and basic facts 5
2. Deformation theory 7
3. Parabolic Higgs bundles and gauge theory 9
Chapter 3. Morse theory on the moduli space 11
1. The Morse function 11
2. Fixed points of the Sl action on the moduli space 12
3. Morse indices 14
4. Rank three parabolic Higgs bundles 16
5. Laumon s Theorem for parabolic Higgs bundles 16
Chapter 4. Parabolic triples 19
1. Definitions and basic facts 19
2. Parabolic Higgs bundles and parabolic triples 20
3. Extensions and deformations of parabolic triples 21
Chapter 5. Critical values and flips 25
1. Critical values 25
2. Crossing critical values and universal extensions 26
3. Flips 28
Chapter 6. Parabolic triples with ri = 2 and r2 = 1 33
1. Flips 33
2. Poincare polynomial of moduli of triples 35
Chapter 7. Critical submanifolds of type (1,1,1) 39
1. Description of the critical submanifolds 39
2. The sum for fixed zu. 42
3. The sum over zu. 44
Chapter 8. Critical submanifolds of type (1,2) 47
1. Description of the critical submanifolds 47
2. The sum for fixed {w,e). 48
3. The sum over vj and e. 49
Chapter 9. Critical submanifolds of type (2,1) 51
1. Description of the critical submanifolds 51
2. The sum for fixed {w,e). 53
3. The sum over w and e. 53
V
vi CONTENTS
Chapter 10. Betti numbers of the moduli space of rank three parabolic
bundles 57
1. Notation 57
2. Holla s formula 58
3. The rank 3 case 58
Chapter 11. Betti numbers of the moduli space of rank three parabolic Higgs
bundles 63
1. Poincare polynomial 63
2. Special low genus cases 64
Chapter 12. The fixed determinant case 67
1. Preliminaries 67
2. Morse indices 68
3. Critical submanifolds of type (1,1,1) 69
4. Parabolic triples of fixed determinant 72
5. Critical submanifolds of type (1, 2) and (2,1) 75
6. Critical submanifolds of type (3) 76
7. Betti numbers of the fixed determinant moduli space 76
Bibliography 79
|
| adam_txt |
Contents
Chapter 1. Introduction 1
Chapter 2. Parabolic Higgs bundles 5
1. Definitions and basic facts 5
2. Deformation theory 7
3. Parabolic Higgs bundles and gauge theory 9
Chapter 3. Morse theory on the moduli space 11
1. The Morse function 11
2. Fixed points of the Sl action on the moduli space 12
3. Morse indices 14
4. Rank three parabolic Higgs bundles 16
5. Laumon's Theorem for parabolic Higgs bundles 16
Chapter 4. Parabolic triples 19
1. Definitions and basic facts 19
2. Parabolic Higgs bundles and parabolic triples 20
3. Extensions and deformations of parabolic triples 21
Chapter 5. Critical values and flips 25
1. Critical values 25
2. Crossing critical values and universal extensions 26
3. Flips 28
Chapter 6. Parabolic triples with ri = 2 and r2 = 1 33
1. Flips 33
2. Poincare polynomial of moduli of triples 35
Chapter 7. Critical submanifolds of type (1,1,1) 39
1. Description of the critical submanifolds 39
2. The sum for fixed zu. 42
3. The sum over zu. 44
Chapter 8. Critical submanifolds of type (1,2) 47
1. Description of the critical submanifolds 47
2. The sum for fixed {w,e). 48
3. The sum over vj and e. 49
Chapter 9. Critical submanifolds of type (2,1) 51
1. Description of the critical submanifolds 51
2. The sum for fixed {w,e). 53
3. The sum over w and e. 53
V
vi CONTENTS
Chapter 10. Betti numbers of the moduli space of rank three parabolic
bundles 57
1. Notation 57
2. Holla's formula 58
3. The rank 3 case 58
Chapter 11. Betti numbers of the moduli space of rank three parabolic Higgs
bundles 63
1. Poincare polynomial 63
2. Special low genus cases 64
Chapter 12. The fixed determinant case 67
1. Preliminaries 67
2. Morse indices 68
3. Critical submanifolds of type (1,1,1) 69
4. Parabolic triples of fixed determinant 72
5. Critical submanifolds of type (1, 2) and (2,1) 75
6. Critical submanifolds of type (3) 76
7. Betti numbers of the fixed determinant moduli space 76
Bibliography 79 |
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| author | García-Prada, Oscar 1960- Gothen, Peter B. Muñoz, Vicente |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV022423000 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:26:21Z |
| indexdate | 2024-07-09T20:57:16Z |
| institution | BVB |
| isbn | 9780821839720 |
| language | English |
| lccn | 2007060665 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015631292 |
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| physical | VII, 80 S. |
| publishDate | 2007 |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | García-Prada, Oscar 1960- Verfasser (DE-588)142082163 aut Betti numbers of the moduli space of rank 3 parabolic Higgs bundles O. García-Prada ; P.B. Gathen ; V. Muñoz Providence, R.I. American Mathematical Society 2007 VII, 80 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 879 "May 2007, volume 187, number 879 (end of volume)." Includes bibliographical references Geometria algébrica larpcal Moduli spaces gtt Vectorbundels gtt Vector bundles Moduli theory Vektorraumbündel (DE-588)4187470-5 gnd rswk-swf Modultheorie (DE-588)4170336-4 gnd rswk-swf Vektorraumbündel (DE-588)4187470-5 s Modultheorie (DE-588)4170336-4 s DE-604 Gothen, Peter B. Verfasser aut Muñoz, Vicente Verfasser aut Memoirs of the American Mathematical Society 879 (DE-604)BV008000141 879 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015631292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | García-Prada, Oscar 1960- Gothen, Peter B. Muñoz, Vicente Betti numbers of the moduli space of rank 3 parabolic Higgs bundles Memoirs of the American Mathematical Society Geometria algébrica larpcal Moduli spaces gtt Vectorbundels gtt Vector bundles Moduli theory Vektorraumbündel (DE-588)4187470-5 gnd Modultheorie (DE-588)4170336-4 gnd |
| subject_GND | (DE-588)4187470-5 (DE-588)4170336-4 |
| title | Betti numbers of the moduli space of rank 3 parabolic Higgs bundles |
| title_auth | Betti numbers of the moduli space of rank 3 parabolic Higgs bundles |
| title_exact_search | Betti numbers of the moduli space of rank 3 parabolic Higgs bundles |
| title_exact_search_txtP | Betti numbers of the moduli space of rank 3 parabolic Higgs bundles |
| title_full | Betti numbers of the moduli space of rank 3 parabolic Higgs bundles O. García-Prada ; P.B. Gathen ; V. Muñoz |
| title_fullStr | Betti numbers of the moduli space of rank 3 parabolic Higgs bundles O. García-Prada ; P.B. Gathen ; V. Muñoz |
| title_full_unstemmed | Betti numbers of the moduli space of rank 3 parabolic Higgs bundles O. García-Prada ; P.B. Gathen ; V. Muñoz |
| title_short | Betti numbers of the moduli space of rank 3 parabolic Higgs bundles |
| title_sort | betti numbers of the moduli space of rank 3 parabolic higgs bundles |
| topic | Geometria algébrica larpcal Moduli spaces gtt Vectorbundels gtt Vector bundles Moduli theory Vektorraumbündel (DE-588)4187470-5 gnd Modultheorie (DE-588)4170336-4 gnd |
| topic_facet | Geometria algébrica Moduli spaces Vectorbundels Vector bundles Moduli theory Vektorraumbündel Modultheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015631292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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