**SMF/AMS Texts and Monographs**

Volume: 11;
2005;
109 pp;
Softcover

MSC: Primary 14;
**Print ISBN: 978-0-8218-3165-6
Product Code: SMFAMS/11**

List Price: $46.00

Individual Member Price: $36.80

#### Supplemental Materials

# Complex Tori and Abelian Varieties

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*Olivier Debarre*

A co-publication of the AMS and Société Mathématique de France

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 co-published 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.

#### Reviews & Endorsements

The present text offers a concise, elegant and intelligible introduction to the fascinating theory of complex tori and complex abelian varieties in its various aspects. ...the author manages to combine the classical theory and the more recent developments in the theory of complex abelian varieties in a very natural, efficient and comprehensible fashion. ...the present book will turn out to be a treasury of mathematical education and culture, and a perfect starter for more advanced and broader studies.

-- Zentralblatt MATH