| Introduction Chapter 1. Classical Hodge Theory 1. Algebraic Varieties 2. Complex Manifolds 3. A Comparison Between Algebraic Varieties and Analytic Spaces 4. Complex Manifolds as C Manifolds 5. Connections on Holomorphic Vector Bundles 6. Hermitian Manifolds 7. Kahler Manifolds 8. Line Bundles and Divisors 9. The Kodaira Vanishing Theorem 10. Monodromy Chapter 2. Periods of Integrals on Algebraic Varieties 1. Classifying Space 2. Complex Tori 3. The Period Mapping 4. Variation of Hodge Structures 5. Torelli Theorems 6. Infinitesimal Variation of Hodge Structures Chapter 3. Torelli Theorems 1. Algebraic Curves 2. The Cubic Threefold 3. K3 Surfaces and Elliptic Pencils 4. Hypersurfaces 5. Counterexamples to Torelli Theorems Chapter 4. Mixed Hodge Structures 1. Definition of mixed Hodge structures 2. Mixed Hodge structure on the Cohomology of a Complete Variety with Normal Crossings 3. Cohomology of Smooth Varieties 4. The Invariant Subspace Theorem 5. Hodge Structure on the Cohomology of Smooth Hypersurfaces 6. Further Development of the Theory of Mixed Hodge Structures Chapter 5. Degenerations of Algebraic Varieties 1. Degenerations of Manifolds 2. The Limit Hodge Structure 3. The Clemens-Schmid Exact Sequence 4. An Application of the Clemens-Schmid Exact Sequence to the Degeneration of Curves 5. An Application of the Clemens-Schmid Exact Sequence to Surface Degenerations. The Relationship Between the Numerical Invariants of the Fibers Xt and X0 6. The Epimorphicity of the Period Mapping for K3 Surfaces Comments on the bibliography References Index |
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