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极值Kähler度量引论（影印版）

暂无简介

作者：

Gábor Székelyhidi

定价：

99.00 元

出版时间：

2023-03-24

ISBN：

978-7-04-059304-4

物料号：

59304-00

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

重点项目：

暂无

版面字数：

350千字

开本：

特殊

装帧形式：

精装

页数：

暂无

最新
印次时间：

2023年01月

目录
- 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