Algebraic Geometry over the Complex Numbers
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Beschreibung
Preface
Part 1. A Quick Tour
1. Plane Curves
Part 2. Sheaves and Geometry
2. Manifolds and Varieties via Sheaves
3. Basic Sheaf Theory
4. Sheaf Cohomology
5. De Rham Cohomoloy of Manifolds
6. Riemann Surfaces
7. Simplicial Methods
Part 3. Hodge Theory
8. The Hodge Theorem for Riemann Manifolds
9. Toward Hodge Theory for Complex Manifolds
10. Kahler Manifolds
11. Homological Methods in Hodge Theory
12. A Little Algebraic Surface Theory
13. Topology of Families
14. The Hard Lefschez Theorem
Part 4. Coherent Cohomology
15. Coherent Sheaves on Projective Space
16. Computation of Some Hodge Numbers
17. Deformation Invariance of Hodge Numbers
Part 5. A Glimpse Beyond
18. Analogies and Conjectures
Bibliography
Index
Part 1. A Quick Tour
1. Plane Curves
Part 2. Sheaves and Geometry
2. Manifolds and Varieties via Sheaves
3. Basic Sheaf Theory
4. Sheaf Cohomology
5. De Rham Cohomoloy of Manifolds
6. Riemann Surfaces
7. Simplicial Methods
Part 3. Hodge Theory
8. The Hodge Theorem for Riemann Manifolds
9. Toward Hodge Theory for Complex Manifolds
10. Kahler Manifolds
11. Homological Methods in Hodge Theory
12. A Little Algebraic Surface Theory
13. Topology of Families
14. The Hard Lefschez Theorem
Part 4. Coherent Cohomology
15. Coherent Sheaves on Projective Space
16. Computation of Some Hodge Numbers
17. Deformation Invariance of Hodge Numbers
Part 5. A Glimpse Beyond
18. Analogies and Conjectures
Bibliography
Index
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