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Algebraic Geometry over the Complex Numbers

Algebraic Geometry over the Complex Numbers
Catalogue Information
Field name Details
Dewey Class 516.35
Title Algebraic Geometry over the Complex Numbers (EB) / by Donu Arapura.
Author Arapura, Donu
Other name(s) SpringerLink (Online service)
Publication Boston, MA : : Springer US, , 2012.
Physical Details XII, 329p. 17 illus., 1 illus. in color. : online resource.
Series Universitext 0172-5939
ISBN 9781461418092
Summary Note This textbook is a strong addition to existing introductory literature on algebraic geometry. The authorâs treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is also 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 this textbook: - 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. âAlgebraic Geometry over the Complex Numbersâ 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.:
Contents note Preface -- 1. Plane Curves -- 2. Manifolds and Varieties via Sheaves -- 3. More Sheaf Theory -- 4. Sheaf Cohomology -- 5. de Rham Cohomoloy of Manifolds -- 6. Riemann Surfaces -- 7. Simplicial Methods -- 8. The Hodge Theorem for Riemann Manifolds -- 9. Toward Hodge Theory for Complex Manifolds -- 10. Kahler Manifolds -- 11. A Little Algebraic Surface Theory -- 12. Hodge Structures and Homological Methods -- 13. Topology of Families -- 14. The Hard Lefschez Theorem -- 15. Coherent Sheaves -- 16. Computation of Coherent Sheaves -- 17. Computation of some Hodge numbers -- 18. Deformation Invariance of Hodge Numbers -- 19. Analogies and Conjectures.- References -- Index.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site http://dx.doi.org/10.1007/978-1-4614-1809-2
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