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MARC 21

Algebraic Geometry over the Complex Numbers
Tag	Description
020	$a9781461418092
082	$a516.35
099	$aOnline Resource: Springer
100	$aArapura, Donu.$d1958-
245	$aAlgebraic Geometry over the Complex Numbers$hEB$cby Donu Arapura.
260	$aBoston, MA$bSpringer US$c2012.
300	$aXII, 329 pages, 17 illus., 1 illus. in color.$bonline resource.
336	$atext
338	$aonline resource
440	$aUniversitext,$x0172-5939
505	$aPreface -- 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.-Â References -- Index.
520	$aThis 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
710	$aSpringerLink (Online service)
830	$aUniversitext,
856	$uhttp://dx.doi.org/10.1007/978-1-4614-1809-2