Algebraic geometry III. Complex algebraic varieties. Algebraic curves and their Jacobians

Contents......Page all_4435_to_00273.cpc0004.djvu
Introduction......Page all_4435_to_00273.cpc0006.djvu
§1. Algebraic Varieties......Page all_4435_to_00273.cpc0014.djvu
§2. Complex Manifolds......Page all_4435_to_00273.cpc0019.djvu
§3. A Comparison Between Algebraic Varieties and Analytic Spaces......Page all_4435_to_00273.cpc0022.djvu
§4. Complex Manifolds as C^\\infty Manifolds......Page all_4435_to_00273.cpc0027.djvu
§5. Connections on Holomorphic Vector Bundles......Page all_4435_to_00273.cpc0031.djvu
§6. Hermitian Manifolds......Page all_4435_to_00273.cpc0036.djvu
§7. Kähler Manifolds......Page all_4435_to_00273.cpc0041.djvu
§8. Line Bundles and Divisors......Page all_4435_to_00273.cpc0052.djvu
§9. The Kodaira Vanishing Theorem......Page all_4435_to_00273.cpc0057.djvu
§10. Monodromy......Page all_4435_to_00273.cpc0063.djvu
§1. Classifying Space......Page all_4435_to_00273.cpc0069.djvu
§2. Complex Tori......Page all_4435_to_00273.cpc0080.djvu
§3. The Period Mapping......Page all_4435_to_00273.cpc0087.djvu
§4. Variation of Hodge Structures......Page all_4435_to_00273.cpc0091.djvu
§5. Torelli Theorems......Page all_4435_to_00273.cpc0092.djvu
§6. Infinitesimal Variation of Hodge Structures......Page all_4435_to_00273.cpc0100.djvu
§1. Algebraic Curves......Page all_4435_to_00273.cpc0103.djvu
§2. The Cubic Threefold......Page all_4435_to_00273.cpc0111.djvu
§3. K3 Surfaces and Elliptic Pencils......Page all_4435_to_00273.cpc0118.djvu
§4. Hypersurfaces......Page all_4435_to_00273.cpc0132.djvu
§5. Counterexamples to Torelli Theorems......Page all_4435_to_00273.cpc0143.djvu
§1. Definition of mixed Hodge structures......Page all_4435_to_00273.cpc0146.djvu
§2. Mixed Hodge structure on the Cohomology of a Complete Variety with Normal Crossings......Page all_4435_to_00273.cpc0152.djvu
§3. Cohomology of Smooth Varieties......Page all_4435_to_00273.cpc0159.djvu
§4. The Invariant Subspace Theorem......Page all_4435_to_00273.cpc0168.djvu
§5. Hodge Structure on the Cohomology of Smooth Hypersurfaces......Page all_4435_to_00273.cpc0171.djvu
§6. Further Development of the Theory of Mixed Hodge Structures......Page all_4435_to_00273.cpc0179.djvu
§1. Degenerations of Manifolds......Page all_4435_to_00273.cpc0186.djvu
§2. The Limit Hodge Structure......Page all_4435_to_00273.cpc0191.djvu
§3. The Clemens-Schmid Exact Sequence......Page all_4435_to_00273.cpc0193.djvu
§4. An Application of the Clemens-Schmid Exact Sequence to the Degeneration of Curves......Page all_4435_to_00273.cpc0199.djvu
§5. An Application of the Clemens-Schmid Exact Sequence to Surface Degenerations. The Relationship Between the Numerical Invariants of the Fibers X_t and X_0......Page all_4435_to_00273.cpc0202.djvu
§6. The Epimorphicity of the Period Mapping for K3 Surfaces......Page all_4435_to_00273.cpc0208.djvu
Comments on the bibliography......Page all_4435_to_00273.cpc0214.djvu
References......Page all_4435_to_00273.cpc0216.djvu
Contents......Page all_4435_to_00273.cpc0222.djvu
1.1. Theory of Burnchall-Chaundy-Krichever......Page all_4435_to_00273.cpc0224.djvu
1.2. Deformation of Commuting Differential Operators......Page all_4435_to_00273.cpc0227.djvu
1.3. Kadomtsev-Petviashvili Equations......Page all_4435_to_00273.cpc0229.djvu
1.4. Finite Dimensional Solutions of the KP Hierarchy......Page all_4435_to_00273.cpc0230.djvu
1.5. Solutions of the Toda Lattice......Page all_4435_to_00273.cpc0231.djvu
1.6. Solution of Algebraic Equations Using Theta-Constants......Page all_4435_to_00273.cpc0233.djvu
2.1. Varieties of Special Divisors and Linear Systems......Page all_4435_to_00273.cpc0235.djvu
2.2. The Brill-Noether Matrix. The Brill-Noether Numbers......Page all_4435_to_00273.cpc0236.djvu
2.3. Existence of Special Divisors......Page all_4435_to_00273.cpc0237.djvu
2.5. Special Curves. The General Case......Page all_4435_to_00273.cpc0238.djvu
2.7. Infinitesimal Theory of Special Linear Systems......Page all_4435_to_00273.cpc0240.djvu
2.8. Gauss Mappings......Page all_4435_to_00273.cpc0242.djvu
2.9. Sharper Bounds on Dimensions......Page all_4435_to_00273.cpc0244.djvu
2.10. Tangent Cones......Page all_4435_to_00273.cpc0245.djvu
3.1. Unbranched Double Covers......Page all_4435_to_00273.cpc0246.djvu
3.2. Prymians and Prym Varieties......Page all_4435_to_00273.cpc0247.djvu
3.3. Polarization Divisor......Page all_4435_to_00273.cpc0249.djvu
3.4. Singularities of the Polarization Divisor......Page all_4435_to_00273.cpc0252.djvu
3.5. Differences Between Prymians and Jacobians......Page all_4435_to_00273.cpc0254.djvu
3.6. The Prym Map......Page all_4435_to_00273.cpc0255.djvu
4.1. The Variety of Jacobians......Page all_4435_to_00273.cpc0256.djvu
4.2. The Andreotti-Meyer Subvariety......Page all_4435_to_00273.cpc0257.djvu
4.3. Kummer Varieties......Page all_4435_to_00273.cpc0258.djvu
4.4. Reducedness of \\Theta \\cap (\\Theta + p) and Trisecants......Page all_4435_to_00273.cpc0259.djvu
4.5. The Characterization of Novikov-Krichever......Page all_4435_to_00273.cpc0261.djvu
4.6. Schottky Relations......Page all_4435_to_00273.cpc0262.djvu
References......Page all_4435_to_00273.cpc0263.djvu
Index......Page all_4435_to_00273.cpc0266.djvu