從全純函式到複流形

《從全純函式到複流形》是2009年世界圖書出版公司出版的圖書，由弗里切編寫。

基本介紹

• 書名：從全純函式到複流形
• ISBN：7510004713, 9787510004711
• 出版社：世界圖書出版公司
• 開本：24

圖書信息

出版社: 世界圖書出版公司; 第1版 (2009年6月1日)

外文書名: From Holomorphic Functions to Complex Manifolds

平裝: 392頁

正文語種: 英語

開本: 24

ISBN: 7510004713, 9787510004711

條形碼: 9787510004711

尺寸: 22.2 x 14.6 x 1.8 cm

重量: 621 g

作者簡介

作者：(德國)弗里切(Fritzsche.K.)

內容簡介

《從全純函式到複流形(英文版)》是一部介紹複流形理論的入門書籍。作者用儘可能簡單的方法使讀者熟悉多變數複分析中的重要分支和方法，所以避免出現比較抽象的概念，如，層、凝聚和高維上同調等，僅運用了基本方法冪級數、正則向量叢和一維上閉鏈。然而，解析集Remmert-Stein定理，正則向量叢中的截面空間有限定理以及Levi問題解這些深層次的都得到了完整的證明。每章的結束都有大量的例子和練習。具備實分析、代數、拓撲以及單變數理論知識就可以完全讀懂這《從全純函式到複流形(英文版)》。《從全純函式到複流形(英文版)》可以作為學習多變數的入門教程，也是一本很好的參考書。

讀者對象：《從全純函式到複流形(英文版)》適用於數學專業的廣大師生。

目錄

Preface

Ⅰ Holomorphic Functions

1.Complex Geometry

Real and Complex Structures

Hermitian Forms and Inner Products

Balls and Polydisks

Connectedness

Reinhardt Domains

2.Power Series

Polynomials

Convergence

Power Series

3.Complex Differentiable Functions

The Complex Gradient

Weakly Holomorphic Functions

Holomorphic Functions

4.The Cauchy Integral

The Integral Formula

Holomorphy of the Derivatives

The Identity Theorem

5.The Hartogs Figure

Expansion in Reinhardt Domains

Hartogs Figures

6.The Cauchy-Riemann Equations

Real Differentiable Functions

Wirtinger's Calculus

The Cauchy-Riemann Equations

7.Holomorphic Maps

The Jacobian

Chain Rules

Tangent Vectors

The Inverse Mapping

8.Analytic Sets

Analytic Subsets

Bounded Holomorphic Functions

Regular Points

Injective Holomorphic Mappings

Ⅱ Domains of Holomorphy

1.The Continuity Theorem

General Hartogs Figures

Removable Singularities

The Continuity Principle

Hartogs Convexity

Domains of Holomorphy

2.Plurisubharmonic Functions

Subharmonic Functions

The Maximum Principle

Differentiable Subharmonic Functions

Plurisubharmonic Functions

The Levi Form

Exhaustion Functions

3.Pseudoconvexity

Pseudoconvexity

The Boundary Distance

Properties of Pseudoconvex Domains

4.Levi Convex Boundaries

Boundary Functions

The Levi Condition

Affine Convexity

A Theorem of Levi

5.Holomorphic Convexity

Affine Convexity

Holomorphic Convexity

The Cartan-Thullen Theorem

6.Singular Functions

Normal Exhaustions

Unbounded Holomorphic Functions

Sequences

7.Examples and Applications

Domains of Holomorphy

Complete Reinhardt Domains

Analytic Polyhedra

8.Riemann Domains over Cn

Riemann Domains

Union of Riemann Domains

9.The Envelope of Holomorphy

Holomorphy on Riemann Domains

Envelopes of Holomorphy

Pseudoconvexity

Boundary Points

Analytic Disks

Ⅲ Analytic Sets

1.The Algebra of Power Series

The Banach Algebra Bt

Expansion with Respect to zt

Convergent Series in Banach Algebras

Convergent Power Series

Distinguished Directions

2.The Preparation Theorem

Division with Remainder in Bt

The Weierstrass Condition

Weierstrass Polynomials

Weierstrass Preparation Theorem

3.Prime Factorization

Unique Factorization

Gauss's Lemma

Factorization in Hn

Hensel's Lemma

The Noetherian Property

4.Branched Coverings

Germs

Pseudopolynomials

Euclidean Domains

The Algebraic Derivative

Symmetric Polynomials

The Discriminant

Hypersurfaces

The Unbranched Part

Decompositions

Projections

5.Irreducible Components

Embedded-Analytic Sets

Images of Embedded Analytic Sets

Local Decomposition

Analyticity

The Zariski Topology

Global Decompositions

6.Regular and Singular Points

Compact Analytic Sets

Embedding of Analytic Sets

Regular Points of an Analytic Set

The Singular Locus

Extending Analytic Sets

The Local Dimension

Ⅳ Complex Manifolds

1.The Complex Structure

Complex Coordinates

Holomorphic Functions

Riemann Surfaces

Holomorphic Mappings

Cartesian Products

Analytic Subsets

Differentiable Functions

Tangent Vectors

The Complex Structure on the Space of Derivations

The Induced Mapping

Immersions and Submersions

Gluing

2.Complex Fiber Bundles

Lie Groups and Transformation Grot ps

Fiber Bt ndles

Equivalence

Complex Vector Bundles

Standard Constructions

Lifting of Bundles

Subbundles and Quotients

3. Cehomolcgy

Cohomology Groups

Refinements

Acyclic Coverings

Generalizations

The Singular Cohomology

4. Meromorphic Functions and Divisors

The Ring of Germs

Analytic Hypersurfaces

Meromorphic Functions

Divisors

Associated Line Bundles

Meromorphic Sections

5. Quotients and Submanifolds

Topological Quotients

Analytic Decompositions

Properly Discontinuously Acting Groups

Complex Tori

Hopf Manifolds

The Complex Projective Space

Meromorphic Functions

Grassmannian Manifolds

Ⅴ Stein Theory

Ⅵ Kahler Manifolds

Ⅶ Boundary Behavior

References

Index of Notation

Index