Complex Manifolds and Deformation of Complex Structures
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1986, 1986
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| Edition: | 1st ed. 1986 |
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
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| 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