极值Kähler度量引论（影印版）

样章

作者：

Gábor Székelyhidi

定价：

99.00元

ISBN：

978-7-04-059304-4

版面字数：

350.000千字

开本：

特殊

全书页数：

暂无

装帧形式：

精装

重点项目：

暂无

出版时间：

2023-03-24

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

分析

暂无

前辅文
Chapter 1. K¨ahler Geometry
- 1.1. Complex manifolds
- 1.2. Almost complex structures
- 1.3. Hermitian and K¨ahler metrics
- 1.4. Covariant derivatives and curvature
- 1.5. Vector bundles
- 1.6. Connections and curvature of line bundles
- 1.7. Line bundles and projective embeddings
Chapter 2. Analytic Preliminaries
- 2.1. Harmonic functions on Rn
- 2.2. Elliptic differential operators
- 2.3. Schauder estimates
- 2.4. The Laplace operator on K¨ahler manifolds
Chapter 3. K¨ahler-Einstein Metrics
- 3.1. The strategy
- 3.2. The C0- and C2-estimates
- 3.3. The C3- and higher-order estimates
- 3.4. The case c1(M) = 0
- 3.5. The case c1(M) >0
- 3.6. Futher reading
Chapter 4. Extremal Metrics
- 4.1. The Calabi functional
- 4.2. Holomorphic vector fields and the Futaki invariant
- 4.3. The Mabuchi functional and geodesics
- 4.4. Extremal metrics on a ruled surface
- 4.5. Toric manifolds
Chapter 5. Moment Maps and Geometric Invariant Theory
- 5.1. Moment maps
- 5.2. Geometric invariant theory (GIT)
- 5.3. The Hilbert-Mumford criterion
- 5.4. The Kempf-Ness theorem
- 5.5. Relative stability
Chapter 6. K-stability
- 6.1. The scalar curvature as a moment map
- 6.2. The Hilbert polynomial and flat limits
- 6.3. Test-configurations and K-stability
- 6.4. Automorphisms and relative K-stability
- 6.5. Relative K-stability of a ruled surface
- 6.6. Filtrations
- 6.7. Toric varieties
Chapter 7. The Bergman Kernel
- 7.1. The Bergman kernel
- 7.2. Proof of the asymptotic expansion
- 7.3. The equivariant Bergman kernel
- 7.4. The algebraic and geometric Futaki invariants
- 7.5. Lower bounds on the Calabi functional
- 7.6. The partial C0-estimate
Chapter 8. CscK Metrics on Blow-ups
- 8.1. The basic strategy
- 8.2. Analysis in weighted spaces
- 8.3. Solving the non-linear equation when n > 2
- 8.4. The case when n = 2
- 8.5. The case when M admits holomorphic vector fields
- 8.6. K-stability of cscK manifolds
Bibliography
Index