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Complex Tori and Abelian Varieties
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Complex Tori and Abelian Varieties

Complex Tori and Abelian Varieties

Volume 11

Olivier Debarre - Collection SMF/AMS Texts and Monographs

120 pages, parution le 25/08/2005

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

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