Complex Abelian Varieties

Christina Birkenhake, Herbert Lange

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English

Springer Verlag
01 June 2004

Mathematics & Sciences; Groups & group theory

Series: Grundlehren der mathematischen Wissenschaften

The subject of this book is the theory of abelian varieties over the field of complex numbers. It covers the main results of the theory, both classic and recent, in modern language. It is intended to give a comprehensive introduction to the field, but also to serve as a reference. The focal topics are the projective embeddings of an abelian variety, their equations and geometric properties. Moreover several moduli spaces of abelian varieties with additional structure are constructed. Some special results on Jacobians and Prym varieties allow applications to the theory of algebraic curves. The second edition contains five new chapters which present some of the most important recent result on the subject. Among them are results on automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture.

By: Christina Birkenhake, Herbert Lange
Imprint: Springer Verlag
Country of Publication: Germany
Edition: 2nd Revised edition
Volume: v. 302
Dimensions: Height: 235mm, Width: 155mm, Spine: 34mm
Weight: 2.400kg
ISBN: 9783540204886
ISBN 10: 3540204881
Series: Grundlehren der mathematischen Wissenschaften
Pages: 656
Publication Date: 01 June 2004
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active

Reviews for Complex Abelian Varieties

"From the reviews: ""… the authors have somehow managed to make it unique in several respects: not only is it far more readable than most of other book on the subject, but it is also much more complete. It is, in my opinion, a very valuable reference book … . […] …prerequisites are kept to a minimum. Very little background in algebraic geometry is necessary, almost all proofs are complete and accessible references are provided whenever they are not. …Olivier Debarre in Mathematical Reviews, 1994 ""It is a great reference and textbook, detailed, very up-to-date, thorough, clearly written and perfectly arranged."" W. Kleinert in Zentralblatt MATH, 1993 ""… written in an understandable and systematical way and can be recommended to all mathematicians and physicists interested in the subject."" Newsletter of the European Mathematical Society, 1993 From the reviews of the second edition: ""This book aims to be a course in Lie groups that can be covered in one year with a group of seasoned graduate students. … offers a wealth of complementary, partly quite recent material that is not found in any other textbook on Lie groups. … this book covers an unusually wide spectrum of topics … . the entire presentation is utmost thorough, comprehensive, lucid and absolutely user-friendly. … All together, this graduate text his a highly interesting, valuable and welcome addition … . (Werner Kleinert, Zentralblatt MATH, Vol. 1053, 2005) From the reviews of the second edition: ""This is the second, substantially extended edition of the book … . The book well deserves to become a standard reference for more researchers working or interested in the theory of abelian varieties."" (Fumio Hazama, Mathematical Reviews, 2005c) ""The book under review is the second, essentially augmented edition of the original standardtext, which now also reflects some of the very recent developments. … the bibliography has been accordingly up-dated and enhanced. … Summing up, the second, amply enlarged and up-dated edition of this outstanding standard monograph on complex abelian varieties has increased its utility in a significant degree, and its leading position among the existing books on the subject has been evidently strengthened."" (Werner Kleinert, Zentralblatt MATH, Vol. 1056, 2005)"