Algebraic geometry over the complex numbers / Donu Arapura.

Format:

Book

Author/Creator:

Arapura, Donu, 1958-

Series:

Universitext

Universitext, 0172-5939

Language:

English

Subjects (All):

Geometry, Algebraic.

Numbers, Complex.

Physical Description:

xii, 329 pages : illustrations ; 23 cm.

Place of Publication:

New York : Springer, [2012]

Summary:

Algebraic Geometry over the Complex Numbers is a strong addition to existing introductory literature on algebraic geometry. The author's treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is an ideal text for showing students the connections between algebraic geometry, complex geometry, and topology, and brings the reader close to the forefront of research in Hodge theory and related fields.

Unique features of Algebraic Geometry over the Complex Numbers:

Contains a rapid introduction to complex algebraic geometry

Includes background material on topology, manifold theory and sheaf theory

Analytic and algebraic approaches are developed somewhat in parallel

The presentation is easy going, elementary, and well illustrated with examples. This textbook is intended for graduate level courses in algebraic geometry and related fields. It can be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory. Book jacket.

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. Kähler 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.

Notes:

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

ISBN:

9781461418085

1461418089

9781461418092

1461418097

OCLC:

752068464