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» » Complex Tori and Abelian Varieties (SMF / AMS Texts and Monographs, Volume 11)
Complex Tori and Abelian Varieties (SMF / AMS Texts and Monographs, Volume 11)

Author:

Philippe Mazaud,Olivier Debarre

Title:

Complex Tori and Abelian Varieties (SMF / AMS Texts and Monographs, Volume 11)

Category:

Other

PDF ebook size:

1629 kb

ePub ebook size:

1937 kb

Fb2 ebook size:

1282 kb

Other book formats:

lrf mbr rtf doc

Rating:

4.2

ISBN10:

0821831658

ISBN13:

978-0821831656

Publisher:

Amer Mathematical Society (July 12, 2005)

Language:

English

Subcategory:

Science and Mathematics

Pages:

109

Buy Hardcover:

Amazon

Complex Tori and Abelian Varieties (SMF / AMS Texts and Monographs, Volume 11) by Philippe Mazaud,Olivier Debarre

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.



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