Preface Chapter 1.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.Sheaves of Groups 3.Infinitesimal Deformations 4.Exact Sequences 5.Vector Bundles 6.A Theorem of Dolbeault (A fine resolution of θ) Chapter 3.Geometry of Complex Manifolds 1.Hermitian Metrics; K?hler Structures 2.Norms and Dual Forms 3.Connections on Vector Bundles 4.Applications of Results on Elliptic Operators 5.Covariant Differentiation on K?hler Manifolds 6.Curvatures on K?hler Manifolds 7.Vanishing Theorems 8.Hodge Manifolds Chapter 4.Applications of Elliptic 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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