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Algebraic geometry over the complex numbers / Donu Arapura.

By: Arapura, Donu, 1958-.
Material type: TextTextSeries: Universitext: Publisher: New York : Springer, c2012Description: xii, 329 p., E 59.95 ill. ; 23 cm.ISBN: 9781461418085 (pbk. : alk. paper); 1461418089 (pbk. : alk. paper); 9781461418092 (eISBN).Subject(s): Geometry, Algebraic | Numbers, ComplexDDC classification: 516.3/5
Contents:
1. Plane curves -- 2. Manifolds and varieties via sheaves -- 3. More sheaf theory -- 4. Sheaf cohomology -- 5. De Rham cohomology of manifolds -- 6. Riemann surfaces -- 7. Simplicial methods -- 8. The Hodge theorem for Riemannian manifolds -- 9. Toward Hodge theory for complex manifolds -- 10. K�ahler manifolds -- 11. A little algebraic surface theory -- 12. Hodge structures and homological methods -- 13. Topology of families -- 14. The hard Lefschetz theorem -- 15. Coherent sheaves -- 16. Cohomology of coherent sheaves -- 17. Computation of some Hodge numbers -- 18. Deformations and Hodge theory -- 19. Analogies and conjectures.

Includes bibliographical references (p. 321-326) and index.

1. Plane curves -- 2. Manifolds and varieties via sheaves -- 3. More sheaf theory -- 4. Sheaf cohomology -- 5. De Rham cohomology of manifolds -- 6. Riemann surfaces -- 7. Simplicial methods -- 8. The Hodge theorem for Riemannian manifolds -- 9. Toward Hodge theory for complex manifolds -- 10. K�ahler manifolds -- 11. A little algebraic surface theory -- 12. Hodge structures and homological methods -- 13. Topology of families -- 14. The hard Lefschetz theorem -- 15. Coherent sheaves -- 16. Cohomology of coherent sheaves -- 17. Computation of some Hodge numbers -- 18. Deformations and Hodge theory -- 19. Analogies and conjectures.