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复流形(影印版) James Morrow, Kunihiko Kodaira 高等教育出版社
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商品名称:复流形(影印版)
ISBN:9787040630961
出版社:高等教育出版社
出版年月:2025-02
作者:James Morrow, Kunihiko Kodaira
定价:99.00
页码:208
装帧:精装
版次:1
字数:330
开本:16开
套装书:否

本书介绍了Kodaira-Spencer复结构变形理论,给出了Kodaira嵌入定理的原始证明,还包括了Kuranishi的半连续性定理和局部完备性定理。本书适合对抽象复流形及相关知识感兴趣的研究生以及数学研究人员阅读参考。 The main purpose of this book is to give an introduction to the Kodaira-Spencer theory of deformations of complex structures. The original proof of the Kodaira embedding theorem is given showing that the restricted class of K?hler manifolds called Hodge manifolds is algebraic. Included are the semicontinuity theorems and the local completeness theorem of Kuranishi. The book is based on notes taken by James Morrow from lectures given by Kunihiko Kodaira at Stanford University in 1965–1966. Complete references are given for the results that are used from elliptic partial differential equations.

前辅文
Chapter I. Definitions and Examples of Complex Manifolds
  1. Holomorphic Functions
  2. Complex Manifolds and Pseudogroup Structures
  3. Some Examples of Construction (or Description) of Compact Complex Manifolds
  4. Analytic Families; Deformations
Chapter 2. Sheaves and Cohomology
  1. Germs of Functions
  2. Cohomology Groups
  3. Infinitesimal Deformations
  4. Exact Sequences
  5. Vector Bundles
  6. A Theorem of Dolbeault (A fine resolution of Ø)
Chapter 3. Geometry of Complex Manifolds
  1. Hermitian Metrics; Kähler Structures
  2. Norms and Dual Forms
  3. Norms for Holomorphic Vector Bundles
  4. Applications of Results on Elliptic Operators
  5. Covariant Differentiation on Kähler Manifolds
  6. Curvatures on Kähler Manifolds
  7. Vanishing Theorems
  8. Hodge Manifolds
Chapter 4. Applications of Eliptic Partial Differential Equations to Deformations
  1. Infinitesimal Deformations
  2. An Existence Theorem for Deformations I. (No Obstructions)
  3. An Existence Theorem for Deformations II. (Kuranishi's Theorem)
  4. Stability Theorem
Bibliography
Index
Errata

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