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Kähler metric and moduli spaces
Title:
Kähler metric and moduli spaces
Author:
Ochiai, Takushiro, editor.
ISBN:
9781483214672
Physical Description:
1 online resource (472 pages)
Series:
Advanced Studies in Pure Mathematics ; 18-II
Advanced studies in pure mathematics (Tokyo, Japan) ; 18-II.
General Note:
"Symposia will be provisionally based at the Department of Mathematics of Nagoya Univeristy, and the proceedings of the symposia will be published under the title Advanced studies in pure mathematics."
Contents:
Front Cover; Kähler 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-Kähler metrics and Calabi's Conjecture; 2. Einstein-Kähler 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-Kähler 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-Kähler metrics I; 7. Existence of Einstein-Kähler metrics II; Appendix; References; Chapter 3. On Tangent Sheaves of Minimal Varieties; 1. Terminologies; 2. Construction of degenerate Einstein-Kähler metrics; 3. Stability for tangent sheaves of minimal varieties; 4. An inequality between Chern numbers; 5. A criterion for stability; References.
Chapter 4. Einstein Kähler Metrics of Negative Ricci Curvature on Open Kahler ManifoldsIntroduction; 1. Calabi's construction; 2. V-manifolds; 3. Schauder estimates; 4. Monge-Ampère equations on V-manifolds; 5. On quasi-projective manifolds; 6. Miyaoka-Yau inequality; References; Chapter 5. Ricci-Flat Kähler Metrics on Affine Algebraic Manifolds and Degenerations of Kähler-Einstein K3 Surfaces; Abstract; 0. Introduction; 1. Some Kähler geometry; 2. Ricci-flat Kähler metrics on affine algebraic manifolds; References; Chapter 6. Compact Ricci-Fiat Kähler 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 Kähler-Einstein K3 surfaces; 2. Ricci-flat K3 surfaces with concentrated curvature; References; Chapter 8. Uniformization of Complex Surfaces; Abstract; 0. Introduction; 1. Kähler-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 Kähler structure on moduli spaces; 2.3. Hyperkähler structure of the moduli space; Chapter 3. Twistor Theory and Yang-Mills Connection.
Abstract:
Kähler 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 differential equations. The book discusses basic facts on Einstein metrics in complex geometry; Einstein-Kähler metrics with positive or non-positive Ricci curvature; Yang-Mills connections; and Einstein-Hermitian metrics. The text then describes the tangent sheaves of minimal varieties; Ricci-Flat Kähler metrics on affi.
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Electronic Access:
ScienceDirect https://www.sciencedirect.com/science/book/9780120010110Available:*
Shelf Number | Item Barcode | Shelf Location | Status |
|---|---|---|---|
| QA649 .K345 1990 EB | 1181409-1001 | Elsevier E-Book Collections | Searching... |
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