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Algebraic Geometry over the Complex Numbers

BuchKartoniert, Paperback
329 Seiten
Englisch
Springererschienen am10.02.20122012
This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject.mehr
Verfügbare Formate
BuchKartoniert, Paperback
EUR80,24
E-BookPDF1 - PDF WatermarkE-Book
EUR80,24

Produkt

KlappentextThis is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject.
ZusammenfassungThis book provides a rapid introduction to complex algebraic geometry. It combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas.
Details
ISBN/GTIN978-1-4614-1808-5
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2012
Erscheinungsdatum10.02.2012
Auflage2012
ReiheUniversitext
Seiten329 Seiten
SpracheEnglisch
Gewicht584 g
IllustrationenXII, 329 p. 17 illus., 1 illus. in color.
Artikel-Nr.11434399

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr
Kritik
From the reviews:

"Book provides a very lucid, vivid, and versatile first introduction to algebraic geometry, with strong emphasis on its transcendental aspects. The author provides a broad panoramic view of the subject, illustrated with numerous instructive examples and interlarded with a wealth of hints for further reading. Indeed, the balance between rigor, intuition, and completeness in the presentation of the material is absolutely reasonable for such an introductory course book, and ... it may serve as an excellent guide to the great standard texts in the field." (Werner Kleinert, Zentralblatt MATH, Vol. 1235, 2012)

"Masterful mathematical expositors guide readers along a meaningful journey. ... Every student should read this book first before grappling with any of those bibles. ... This is an advanced book in its own right ... . Arapura's knack for doing things in the simplest possible way and explaining the 'why' makes for much easier reading than one might reasonably expect. Summing Up: Highly recommended. Upper-division undergraduates and above." (D. V. Feldman, Choice, Vol. 50 (5), January, 2013)

"The book under review is a welcome addition to the literature on complex algebraic geometry. The approach chosen by the author balances the algebraic and transcendental approaches and unifies them by using sheaf theoretical methods. ... This is a well-written text ... with plenty of examples to illustrate the ideas being discussed." (Felipe Zaldivar, The Mathematical Association of America, June, 2012)

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Autor

Donu Arapura is a Professor of Mathematics at Purdue University. He received his Ph.D. from Columbia University in 1985. Dr. Arapura's primary research includes algebraic geometry, and he has written and co-written several publications ranging from Hodge cycles to cohomology.
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