An introduction to extremal Kähler metrics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2014]
|
| Series: | Graduate studies in mathematics
volume 152 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvi, 192 Seiten Diagramme |
| ISBN: | 9781470410476 |
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Record in the Search Index
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| adam_text | Titel: An introduction to extremal Kähler metrics
Autor: Székelyhidi, Gábor
Jahr: 2014
Contents
Preface xi
Introduction xiii
Chapter 1. Kähler Geometry 1
§1.1. Complex manifolds 1
§1.2. Almost complex structures 4
§1.3. Hermitian and Kähler metrics 6
§1.4. Covariant derivatives and curvature 10
§1.5. Vector bundles 13
§1.6. Connections and curvature of line bundles 16
§1.7. Line bundles and projective embeddings 19
Chapter 2. Analytic Preliminaries 23
§2.1. Harmonie funetions on Rn 23
§2.2. Elliptic differential Operators 25
§2.3. Schauder estimates 26
§2.4. The Laplace Operator on Kähler manifolds 32
Chapter 3. Kähler-Einstein Metrics 35
§3.1. The strategy 36
§3.2. The C°- and C2-estimates 40
§3.3. The C3- and higher-order estimates 44
§3.4. The case c (M) = 0 47
vii
viii
Contents
§3.5. The case c (M) 0 51
§3.6. Futher reading 53
Chapter 4. Extremal Metrics 57
§4.1. The Calabi functional 57
§4.2. Holomorphic vector Heids and the Futaki invariant 62
§4.3. The Mabuchi functional and geodesics 67
§4.4. Extremal metrics on a ruled surface 71
§4.5. Toric manifolds 76
Chapter 5. Moment Maps and Geometrie Invariant Theory 85
§5.1. Moment maps 85
§5.2. Geometrie invariant theory (GIT) 90
§5.3. The Hilbert-Mumford criterion 94
§5.4. The Kempf-Ness theorem 97
§5.5. Relative stability 101
Chapter 6. K-stability 105
§6.1. The scalar curvature as a moment map 105
§6.2. The Hilbert polynomial and Hat limits 109
§6.3. Test-configurations and K-stability III
§6.4. Automorphisms and relative K-stability 115
§6.5. Relative K-stability of a ruled surface 116
§6.6. Filtrations 120
§6.7. Toric varieties 124
Chapter 7. The Bergman Kernel 129
§7.1. The Bergman kernel 129
§7.2. Proof of the asymptotic expansion 132
§7.3. The equivariant Bergman kernel 138
§7.4. The algebraic and geometric Futaki invariants 140
§7.5. Lower bounds on the Calabi functional 142
§7.6. The partial C°-estimate 150
Chapter 8. CscK Metrics on Blow-ups 153
§8.1. The basic strategy 153
§8.2. Analysis in weighted spaces 159
§8.3. Solving the non-linear equation when n 2 172
Contents
ix
§8.4. The case when n = 2 174
§8.5. The case when M admits holomorphic vector fields 178
§8.6. K-stability of cscK manifolds 181
Bibliography 185
Index 191
|
| any_adam_object | 1 |
| author | Székelyhidi, Gábor 1981- |
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| dewey-tens | 510 - Mathematics |
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| spelling | Székelyhidi, Gábor 1981- Verfasser (DE-588)1059230887 aut An introduction to extremal Kähler metrics Gábor Székelyhidi Providence, Rhode Island American Mathematical Society [2014] © 2014 xvi, 192 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics volume 152 Differential geometry ... Global differential geometry ... Special Riemannian manifolds (Einstein, Sasakian, etc.) msc Differential geometry ... Global differential geometry ... Hermitian and Kählerian manifolds msc Algebraic geometry ... Algebraic groups ... Geometric invariant theory msc Geometry, Differential Differential geometry ... Global differential geometry ... Special Riemannian manifolds (Einstein, Sasakian, etc.) Differential geometry ... Global differential geometry ... Hermitian and Kählerian manifolds Algebraic geometry ... Algebraic groups ... Geometric invariant theory Kähler-Metrik (DE-588)4622532-8 gnd rswk-swf Kähler-Metrik (DE-588)4622532-8 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1687-4 Graduate studies in mathematics volume 152 (DE-604)BV009739289 152 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027498680&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Székelyhidi, Gábor 1981- An introduction to extremal Kähler metrics Graduate studies in mathematics Differential geometry ... Global differential geometry ... Special Riemannian manifolds (Einstein, Sasakian, etc.) msc Differential geometry ... Global differential geometry ... Hermitian and Kählerian manifolds msc Algebraic geometry ... Algebraic groups ... Geometric invariant theory msc Geometry, Differential Differential geometry ... Global differential geometry ... Special Riemannian manifolds (Einstein, Sasakian, etc.) Differential geometry ... Global differential geometry ... Hermitian and Kählerian manifolds Algebraic geometry ... Algebraic groups ... Geometric invariant theory Kähler-Metrik (DE-588)4622532-8 gnd |
| subject_GND | (DE-588)4622532-8 |
| title | An introduction to extremal Kähler metrics |
| title_auth | An introduction to extremal Kähler metrics |
| title_exact_search | An introduction to extremal Kähler metrics |
| title_full | An introduction to extremal Kähler metrics Gábor Székelyhidi |
| title_fullStr | An introduction to extremal Kähler metrics Gábor Székelyhidi |
| title_full_unstemmed | An introduction to extremal Kähler metrics Gábor Székelyhidi |
| title_short | An introduction to extremal Kähler metrics |
| title_sort | an introduction to extremal kahler metrics |
| topic | Differential geometry ... Global differential geometry ... Special Riemannian manifolds (Einstein, Sasakian, etc.) msc Differential geometry ... Global differential geometry ... Hermitian and Kählerian manifolds msc Algebraic geometry ... Algebraic groups ... Geometric invariant theory msc Geometry, Differential Differential geometry ... Global differential geometry ... Special Riemannian manifolds (Einstein, Sasakian, etc.) Differential geometry ... Global differential geometry ... Hermitian and Kählerian manifolds Algebraic geometry ... Algebraic groups ... Geometric invariant theory Kähler-Metrik (DE-588)4622532-8 gnd |
| topic_facet | Differential geometry ... Global differential geometry ... Special Riemannian manifolds (Einstein, Sasakian, etc.) Differential geometry ... Global differential geometry ... Hermitian and Kählerian manifolds Algebraic geometry ... Algebraic groups ... Geometric invariant theory Geometry, Differential Kähler-Metrik |
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