Algebraic Geometry over the Complex Numbers

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Sprache: Englisch

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Beschreibung

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.

Über den 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.

Zusammenfassung

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

Easy-going style will not intimidate newcomers to algebraic geometry

Includes supplementary material: [...]

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.

Details

Erscheinungsjahr:	2012
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	344
Reihe:	Universitext
Inhalt:	xii 329 S. 16 s/w Illustr. 1 farbige Illustr. 329 p. 17 illus. 1 illus. in color.
ISBN-13:	9781461418085
ISBN-10:	1461418089
Sprache:	Englisch
Herstellernummer:	80014006
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Arapura, Donu
Auflage:	2012
Hersteller:	Springer US Springer New York Universitext
Maße:	235 x 155 x 18 mm
Von/Mit:	Donu Arapura
Erscheinungsdatum:	10.02.2012
Gewicht:	0,585 kg

preigu-id: 106803361