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K�ahler metric and moduli spaces /
K�ahler Metric and Moduli Spaces, Volume 18-II covers survey notes from the expository lectures given during the seminars in the academic year of 1987 for graduate students and mature mathematicians who were not experts on the topics considered during the sessions about partial differenti...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Tokyo, Japan :
Kinokuniya Company Ltd.,
1990.
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| Colección: | Advanced studies in pure mathematics (Tokyo, Japan) ;
18-II. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; K�ahler Metric and Moduli Spaces; Copyright Page; Foreword; Preface to the Present Volume; Table of Contents; Chapter 1. Einstein Metrics in Complex Geometry: An Introduction; 1. Einstein-K�ahler metrics and Calabi's Conjecture; 2. Einstein-K�ahler metrics for compact Riemann surfaces; 3. Birational moduli of algebraic surfaces of general type; 4. Uniformization by Miyaoka-Van de Ven-Yau's inequality; 5. Einstein-Hermitian metrics and stable vector bundles; References; Chapter 2. Einstein-K�ahler Metrics with Positive Ricci Curvature; Introduction.
- 1. Matsushima's obstruction and Kobayashi's semistability2. Futaki's obstruction F; 3. Symplectic geometry and the character F; 4. Chern-Simons invariants and the group lifting of F; 5. The uniqueness theorem; 6. Existence of Einstein-K�ahler metrics I; 7. Existence of Einstein-K�ahler metrics II; Appendix; References; Chapter 3. On Tangent Sheaves of Minimal Varieties; 1. Terminologies; 2. Construction of degenerate Einstein-K�ahler metrics; 3. Stability for tangent sheaves of minimal varieties; 4. An inequality between Chern numbers; 5. A criterion for stability; References.
- Chapter 4. Einstein K�ahler Metrics of Negative Ricci Curvature on Open Kahler ManifoldsIntroduction; 1. Calabi's construction; 2. V-manifolds; 3. Schauder estimates; 4. Monge-Amp�ere equations on V-manifolds; 5. On quasi-projective manifolds; 6. Miyaoka-Yau inequality; References; Chapter 5. Ricci-Flat K�ahler Metrics on Affine Algebraic Manifolds and Degenerations of K�ahler-Einstein K3 Surfaces; Abstract; 0. Introduction; 1. Some K�ahler geometry; 2. Ricci-flat K�ahler metrics on affine algebraic manifolds; References; Chapter 6. Compact Ricci-Fiat K�ahler Manifolds; 1. Bogomolov decomposition.
- 2. Deformation3. Symplectic manifolds; 4. Period map and Weil-Peterson metric; 5. Examples; References; Chapter 7. Moduli of Einstein Metrics on a K3 Surface and Degeneration of Type I; Abstract; 0. Preliminaries; 1. The moduli of K�ahler-Einstein K3 surfaces; 2. Ricci-flat K3 surfaces with concentrated curvature; References; Chapter 8. Uniformization of Complex Surfaces; Abstract; 0. Introduction; 1. K�ahler-Einstein metrics and uniformization; 2. Holomorphic G-structures and uniformization; 3. Numerical characterization of ball quotients for normal surfaces with branch loci.
- 4. GHCS and uniformization of complex surfaces5. Appendix; References; Yang-Mills Connections and Einstein
- Hermitian Metrics; Introduction; Chapter 1. Notation and Preliminaries; 1.1. Yang-Mills functional and Yang-Mills connections; 1.2. Self-dual connections; 1.3. Einstein-Hermitian connections; 1.4. Moment maps; Chapter 2. Local Goometries of Moduli Spaces; 2.1. Smooth structure on moduli space; 2.2. Complex K�ahler structure on moduli spaces; 2.3. Hyperk�ahler structure of the moduli space; Chapter 3. Twistor Theory and Yang-Mills Connection.