| BOOK 2. Schemes and Varieties Chapter V. Schemes 1. The Spec of a Ring 2. Sheaves 3. Schemes 4. Products of Schemes Chapter VI. Varieties 1. Definitions and Examples 2 Abstract and Quasiprojective Varieties 3 Coherent Sheaves 4 Classification of Geometric Objects and Universal Schemes BOOK 3. Complex Algebraic Varieties and Complex Manifolds Chapter VII. The Topology of Algebraic Varieties 1. The Complex Topology 2. Connectedness 3. The Topology of Algebraic Curves 4. Real Algebraic Curves Chapter VIII. Complex Manifolds 1. Definitions and Examples 2. Divisors and Meromorphic Functions 3 Algebraic Varieties and Complex Manifolds 4. Kahler Manifolds Chapter IX. Uniformisation 1. The Universal Cover 2 Curves of Parabolic Type 3 Curves of Hyperbolic Type 4. Uniformising Higher Dimensional Varieties Historical Sketch 1. Elliptic Integrals 2. Elliptic Functions 3. Abelian Integrals 4. Riemann Surfaces 5. The Inversion of Abelian Integrals 6. The Geometry of Algebraic Curves 7. Higher Dimensional Geometry 8. The Analytic Theory of Complex Manifolds 9. Algebraic Varieties over Arbitrary Fields and Schemes References Index |
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