Complex Manifolds and Deformation of Complex Structures

Main Author: Kodaira, K.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 1986, 1986
Edition:1st ed. 1986
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Holomorphic Functions
  • §1.1. Holomorphic Functions
  • §1.2. Holomorphic Map
  • 2 Complex Manifolds
  • §2.1. Complex Manifolds
  • §2.2. Compact Complex Manifolds
  • §2.3. Complex Analytic Family
  • 3 Differential Forms, Vector Bundles, Sheaves
  • §3.1. Differential Forms
  • §3.2. Vector Bundles
  • §3.3. Sheaves and Cohomology
  • §3.4. de Rham’s Theorem and Dolbeault’s Theorem
  • §3.5. Harmonic Differential Forms
  • §3.6. Complex Line Bundles
  • 4 Infinitesimal Deformation
  • §4.1. Differentiable Family
  • §4.2. Infinitesimal Deformation
  • 5 Theorem of Existence
  • §5.1. Obstructions
  • §5.2. Number of Moduli
  • §5.3. Theorem of Existence
  • 6 Theorem of Completeness
  • §6.1. Theorem of Completeness
  • §6.2. Number of Moduli
  • §6.3. Later Developments
  • 7 Theorem of Stability
  • §7.1. Differentiable Family of Strongly Elliptic Differential Operators
  • §7.2. Differentiable Family of Compact Complex Manifolds
  • Appendix Elliptic Partial Differential Operators on a Manifold
  • §1. Distributions on a Torus
  • §2. Elliptic Partial Differential Operators on a Torus
  • §3. Function Space of Sections of a Vector Bundle
  • §4. Elliptic Linear Partial Differential Operators
  • §5. The Existence of Weak Solutions of a Strongly Elliptic Partial Differential Equation
  • §6. Regularity of Weak Solutions of Elliptic Linear Partial Differential Equations