CHAPTER 1
Hoiomorphic Functions
§1.1. Holomorphic Functions
§1.2. Holomorphic Map
CHAPTER 2
Complex Manifolds
§2.1. Complex Manifolds
§2.2. Compact Complex Manifolds
§2.3. Complex Analytic Family
CHAPTER 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
CHAPTER 4
Infinitesimal Deformation
§4.1. Differentiable Family
§4.2. Infinitesimal Deformation
CHAPTER 5
Theorem of Existence
§5.1. Obstructions
§5.2. Number of Moduli
§5.3. Theorem of Existence
CHAPTER 6
Theorem of Completehess
§6.1. Theorem of Completeness
§6.2. Number of Moduli
§6.3. Later Developments
CHAPTER 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 by Daisuke Fujiwara
§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
§7. Elliptic Operators in the Hilbert Space L2(X, B)
§8. C∞ Difterentiability of φ(t)
Bibliography
Index
