Algebraic geometry over the complex numbers / Donu Arapura

Auteur: Arapura, Donu (1958-) - AuteurType de document: Monographie Collection: Universitext Langue: anglaisPays: Etats UnisÉditeur: New York : Springer, cop. 2012Description: 1 vol. (XII-329 p.) : fig. ; 24 cm ISBN: 1461418097 ; br. Résumé: This textbook 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 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. “Algebraic Geometry over the Complex Numbers” 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. (Source : Springer).Bibliographie: Bibliogr. p. 321-326. Index. Sujets MSC: 14-01 Algebraic geometry -- Instructional exposition (textbooks, tutorial papers, etc.)
14C30 Algebraic geometry -- Cycles and subschemes -- Transcendental methods, Hodge theory, Hodge conjecture
14F05 Algebraic geometry -- (Co)homology theory -- Sheaves, derived categories of sheaves and related constructions
14A10 Algebraic geometry -- Foundations -- Varieties and morphisms
30F10 Functions of a complex variable -- Riemann surfaces -- Compact Riemann surfaces and uniformization
32Q15 Several complex variables and analytic spaces -- Complex manifolds -- Kähler manifolds
En-ligne: Springerlink
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Bibliogr. p. 321-326. Index

This textbook 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 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.

“Algebraic Geometry over the Complex Numbers” 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. (Source : Springer)

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