解析几何与代数几何:相同问题,不同方法
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作者(美)杰弗里·麦克尼尔,(罗)米尔恰·穆斯塔塔
出版社高等教育出版社
ISBN9787040510553
出版时间2019-02
装帧精装
开本16开
定价199元
货号1201818206
上书时间2025-01-06
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目录
Preface
Jeffery McNeal and Mircea Mustata
Introduction
Bo Berndtsson
An Introduction to Things
Introduction
Lecture 1. The one-dimensional case
1.1. The 0-equation in one variable
1.2. An alternative proof of the basic identity
1.3. An application: Inequalities of Brunn-Minkowski type
1.4. Regularity -- a disclaimer
Lecture 2. Functional analytic interlude
2.1. Dual formulation of the problem
Lecture 3. The -equation on a complex manifold
3.1. Metrics
3.2. Norms of forms
3.3. Line bundles
3.4. Calculation of the adjoint and the basic identity
3.5. The main existence theorem and L2-estimate for compact manifolds
3.6. Complete Kahler manifolds
Lecture 4. The Bergman kernel
4.1. Generalities
4.2. Bergman kernels associated to complex line bundles
Lecture 5. Singular metrics and the Kawamata-Viehweg vanishing theorem
5.1. The Demailly-Nadel vanishing theorem
5.2. The Kodaira embedding theorem
5.3. The Kawamata-Viehweg vanishing theorem
Lecture 6. Adjunction and extension from divisors
6.1. Adjunction and the currents defined by divisors
6.2. The Ohsawa-Takegoshi extension theorem
Lecture 7. Deformational invariance of plurigenera
7.1. Extension of pluricanonical forms
Bibliography
John P. DAngelo
Real and Complex Geometry meet the Cauchy-Riemann Equations
Preface
Lecture 1. Background material
1. Complex linear algebra
2. Differential forms
3. Solving the Cauchy-Riemann equations
Lecture 2. Complex varieties in real hypersurfaces
1. Degenerate critical points of smooth functions
2. Hermitian symmetry and polarization
3. Holomorphic decomposition
4. Real analytic hypersurfaces and subvarieties
5. Complex varieties, local algebra, and multiplicities
Lecture 3. Pseudoconvexity, the Levi form, and points of finite type
1. Euclidean convexity
2. The Levi form
3. Higher order commutators
4. Points of finite type
5. Commutative algebra
6. A return to finite type
7. The set of finite type points is open
Lecture 4. Kohns algorithm for subelliptic multipliers
1. Introduction
2. Subelliptic estimates
3. Kohns algorithm
4. Kohns algorithm for holomorphic and formal germs
5. Failure of effectiveness for Kohns algorithm
6. Triangular systems
7. Additional remarks
Lecture 5. Connections with partial differential equations
1. Finite type conditions
2. Local regularity for
3. Hypoellipticity, global regularity, and compactness
4. An introduction to L2-estimates
Lecture 6. Positivity conditions
1. Introduction
2. The classes Pk
3. Intermediate conditions
4. The global Canchy-Schwarz inequality
5. A complicated example
6. Stabilization in the bihomogeneous polynomial case
7. Squared norms and proper mappings between balls
8. Holomorphic line bundles
……
内容摘要
本书是我社正在开发的《美国数学会经典影印系列》中的一本，美国数学会的出版物在靠前数学界享有很高声誉，出版了很多影响广泛的数学书。“十三五”期间计划引进的该学会的图书系列涵盖了代数、几何、分析、方程、拓扑、概率、动力系统等所有主要数学分支以及新近发展的数学主题。本书源于以解析几何和代数几何为主题的PCMI暑期学校的一系列讲座。该系列讲座旨在介绍解析几何和代数几何中近期新进展背后所运用的不错技巧。讲座包含了许多说明性的例子、详细的计算和对所提出的主题的新观点，以便增强非专业人士对这些材料的理解。
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