Chapter I Manifolds and Vector Bundles
1. Manifolds
2. Vector Bundles
3. Almost Complex Manifolds and thecS-Operator
Chapter II Sheaf Theory
1. Presheaves and Sheaves
2. Resolutions of Sheaves
3. Cohomology Theory
Appendix A. Cech Cohomology with Coefficients in a Sheaf
ChaptercHI Differential Geometry
1. Hermitian Differential Geometry
2. ThecCanonical Connectioncand Curvaturecofca Hermitian Holomorphic Vector Bundle
3. Chern Classescof Differentiable Vector Bundles
4. Complex Line Bundles
Chapter IV Elliptic Operator Theory
1. Sobolev Spaces
2. Differential Operators
3. Pseudodifferential Operators
4. A Parametrixcfor Elliptic Differential Operators
5. Elliptic Complexes
Chapter V Compact Complex Manifolds
1. Hermitian Exterior Algebraconca Hermitian Vector Space
2. Harmonic Theorycon Compact Manifolds
3. Representations of st(2,cC) on Hermitian Exterior Algebras
4. Differential Operatorsconca Kahier Manifold
5. The Hodge Decomposition Theoremcon Compact Kahler Manifolds
6. ThecHodge-Riemann Bilinear Relationsconca Kahler Manifoldc
Chapter VI Kodaira's Projective Embedding Theorem
1. HodgeManifolds
2. Kodaira's Vanishing Theorem
3. Quadratic Transformations
4. Kodaira's Embedding Theorem
References
Subject Index
Author Index
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