Differential analysis on complex manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
[2008]
|
| Edition: | third edition |
| Series: | Graduate texts in mathematics
65 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 299 Seiten |
| ISBN: | 9781441925350 9780387738925 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804137381653118976 |
|---|---|
| adam_text | CONTENTS
Chapter I Manifolds and Vector Bundles 1
1. Manifolds 2
2. Vector Bundles 12
3. Almost Complex Manifolds and the 3-Operator 27
Chapter II Sheaf Theory 36
1. Presheaves and Sheaves 36
2. Resolutions of Sheaves 42
3. Cohomology Theory 51
4. Cech Cohomology with Coefficients in a Sheaf 63
Chapter III Differential Geometry 65
1. Hermitian Differential Geometry 65
2. The Canonical Connection and Curvature of a Hermitian
Holomorphic Vector Bundle 77
3. Chern Classes of Differentiate Vector Bundles 84
4. Complex Line Bundles 97
xi
xii Contents
Chapter IV Elliptic Operator Theory 108
1. Sobolev Spaces 108
2. Differential Operators 113
3. Pseudodifferential Operators 119
4. A Parametrix for Elliptic Differential Operators 136
5. Elliptic Complexes 144
Chapter V Compact Complex Manifolds 154
1. Hermitian Exterior Algebra on a Hermitian Vector
Space 154
2. Harmonic Theory on Compact Manifolds 163
3. Representations of sl(2, C) on Hermitian Exterior
Algebras 170
4. Differential Operators on a Kahler Manifold 188
5. The Hodge Decomposition Theorem on Compact Kahler
Manifolds 197
6. The Hodge-Riemann Bilinear Relations on a Kahler
Manifold 201
Chapter VI Kodaira s Projective Embedding Theorem 217
1. Hodge Manifolds 217
2. Kodaira s Vanishing Theorem 222
3. Quadratic Transformations 229
4. Kodaira s Embedding Theorem 234
Appendix (by Oscar Garcia-Prada)
Moduli Spaces and Geometric Structures 241
1. Introduction 241
2. Vector Bundles on Riemann Surfaces 243
3. Higgs Bundles on Riemann Surfaces 253
4. Representations of the Fundamental Group 258
5. Non-abelian Hodge Theory 261
6. Representations in U(p, q) and Higgs Bundles 265
Contents xiii
7. Moment Maps and Geometry of Moduli Spaces 269
8. Higher Dimensional Generalizations 276
References 284
Author Index 291
Subject Index 293
|
| adam_txt |
CONTENTS
Chapter I Manifolds and Vector Bundles 1
1. Manifolds 2
2. Vector Bundles 12
3. Almost Complex Manifolds and the 3-Operator 27
Chapter II Sheaf Theory 36
1. Presheaves and Sheaves 36
2. Resolutions of Sheaves 42
3. Cohomology Theory 51
4. Cech Cohomology with Coefficients in a Sheaf 63
Chapter III Differential Geometry 65
1. Hermitian Differential Geometry 65
2. The Canonical Connection and Curvature of a Hermitian
Holomorphic Vector Bundle 77
3. Chern Classes of Differentiate Vector Bundles 84
4. Complex Line Bundles 97
xi
xii Contents
Chapter IV Elliptic Operator Theory 108
1. Sobolev Spaces 108
2. Differential Operators 113
3. Pseudodifferential Operators 119
4. A Parametrix for Elliptic Differential Operators 136
5. Elliptic Complexes 144
Chapter V Compact Complex Manifolds 154
1. Hermitian Exterior Algebra on a Hermitian Vector
Space 154
2. Harmonic Theory on Compact Manifolds 163
3. Representations of sl(2, C) on Hermitian Exterior
Algebras 170
4. Differential Operators on a Kahler Manifold 188
5. The Hodge Decomposition Theorem on Compact Kahler
Manifolds 197
6. The Hodge-Riemann Bilinear Relations on a Kahler
Manifold 201
Chapter VI Kodaira's Projective Embedding Theorem 217
1. Hodge Manifolds 217
2. Kodaira's Vanishing Theorem 222
3. Quadratic Transformations 229
4. Kodaira's Embedding Theorem 234
Appendix (by Oscar Garcia-Prada)
Moduli Spaces and Geometric Structures 241
1. Introduction 241
2. Vector Bundles on Riemann Surfaces 243
3. Higgs Bundles on Riemann Surfaces 253
4. Representations of the Fundamental Group 258
5. Non-abelian Hodge Theory 261
6. Representations in U(p, q) and Higgs Bundles 265
Contents xiii
7. Moment Maps and Geometry of Moduli Spaces 269
8. Higher Dimensional Generalizations 276
References 284
Author Index 291
Subject Index 293 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Wells, Raymond O. 1940- |
| author_GND | (DE-588)120568853 |
| author_facet | Wells, Raymond O. 1940- |
| author_role | aut |
| author_sort | Wells, Raymond O. 1940- |
| author_variant | r o w ro row |
| building | Verbundindex |
| bvnumber | BV023116086 |
| classification_rvk | SK 350 SK 370 SK 780 |
| ctrlnum | (OCoLC)255907419 (DE-599)BVBBV023116086 |
| dewey-full | 515.946 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.946 |
| dewey-search | 515.946 |
| dewey-sort | 3515.946 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | third edition |
| format | Book |
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| id | DE-604.BV023116086 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:50:01Z |
| indexdate | 2024-07-09T21:11:24Z |
| institution | BVB |
| isbn | 9781441925350 9780387738925 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016318610 |
| oclc_num | 255907419 |
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| physical | xiii, 299 Seiten |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Wells, Raymond O. 1940- (DE-588)120568853 aut Differential analysis on complex manifolds third edition New York Springer [2008] © 2008 xiii, 299 Seiten txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 65 Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Differential (DE-588)4149768-5 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 s Differential (DE-588)4149768-5 s 1\p DE-604 Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s 2\p DE-604 Mannigfaltigkeit (DE-588)4037379-4 s 3\p DE-604 Erscheint auch als Online-Ausgabe 978-0-387-73892-5 Graduate texts in mathematics 65 (DE-604)BV000000067 65 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016318610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wells, Raymond O. 1940- Differential analysis on complex manifolds Graduate texts in mathematics Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Differential (DE-588)4149768-5 gnd |
| subject_GND | (DE-588)4031996-9 (DE-588)4037379-4 (DE-588)4012269-4 (DE-588)4149768-5 |
| title | Differential analysis on complex manifolds |
| title_auth | Differential analysis on complex manifolds |
| title_exact_search | Differential analysis on complex manifolds |
| title_exact_search_txtP | Differential analysis on complex manifolds |
| title_full | Differential analysis on complex manifolds |
| title_fullStr | Differential analysis on complex manifolds |
| title_full_unstemmed | Differential analysis on complex manifolds |
| title_short | Differential analysis on complex manifolds |
| title_sort | differential analysis on complex manifolds |
| topic | Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Differential (DE-588)4149768-5 gnd |
| topic_facet | Komplexe Mannigfaltigkeit Mannigfaltigkeit Differenzierbare Mannigfaltigkeit Differential |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016318610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT wellsraymondo differentialanalysisoncomplexmanifolds |