Complex Tori and Abelian Varieties

Volume 11

Olivier Debarre - Collection SMF/AMS Texts and Monographs

120 pages, parution le 25/08/2005

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Résumé

This graduate-level textbook introduces the classical theory of complex tori and abelian varieties, while presenting in parallel more modern aspects of complex algebraic and analytic geometry. Beginning with complex elliptic curves, the book moves on to the higher-dimensional case, giving characterizations from different points of view of those complex tori which are abelian varieties, i.e., those that can be holomorphically embedded in a projective space. This allows, on the one hand, for illuminating the computations of nineteenth-century mathematicians, and on the other, familiarizing readers with more recent theories. Complex tori are ideal in this respect: One can perform "hands-on" computations without the theory being totally trivial.

Standard theorems about abelian varieties are proved, and moduli spaces are discussed. Recent results on the geometry and topology of some subvarieties of a complex torus are also included.

The book contains numerous examples and exercises. It is a very good starting point for studying algebraic geometry, suitable for graduate students and researchers interested in algebra and algebraic geometry.

Titles in this series are copublished with Société Mathématique de France. SMF members are entitled to AMS member discounts.

Readership : Graduate students and research mathematicians interested in algebra and algebraic geometry.

L'auteur - Olivier Debarre

Olivier Debarre, Université Louis Pasteur, Strasbourg, France

Sommaire

Lattices and complex tori
Elliptic curves
Differential forms and de Rham cohomology
Theta functions and divisors
Line bundles, sheaf cohomology, and first Chern class
Abelian varieties
Moduli spaces
Subvarieties of a complex torus

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Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Olivier Debarre
Collection	SMF/AMS Texts and Monographs
Parution	25/08/2005
Nb. de pages	120
Format	17,5 x 25,5
Couverture	Broché
Poids	230g
Intérieur	Noir et Blanc
EAN13	9780821831656
ISBN13	978-0-8218-3165-6