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Field name	Details
Dewey Class	516.35
Title	Complex Abelian Varieties ([EBook]) / by Herbert Lange, Christina Birkenhake.
Author	Lange, Herbert. , 1943-
Added Personal Name	Birkenhake, Christina
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1992.
Physical Details	VIII, 435 pages : online resource.
Series	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 0072-7830 ; ; 302
ISBN	9783662027882
Summary Note	Abelian varieties are special examples of projective varieties. As such theycan be described by a set of homogeneous polynomial equations. The theory ofabelian varieties originated in the beginning of the ninetheenth centrury with the work of Abel and Jacobi. The subject of this book is the theory of abelian varieties over the field of complex numbers, and 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 onJacobians and Prym varieties allow applications to the theory of algebraic curves. The main tools for the proofs are the theta group of a line bundle, introduced by Mumford, and the characteristics, to be associated to any nondegenerate line bundle. They are a direct generalization of the classical notion of characteristics of theta functions.:
Contents note	Notation -- 1 Complex Tori -- 2 Line Bundles on Complex Tori -- 3 Cohomology of Line Bundles -- 4 Abelian Varieties -- 5 Endomorphisms of Abelian Varieties -- 6 Theta and Heisenberg Groups -- 7 Equations for Abelian Varieties -- 8 Moduli -- 9 Moduli Spaces of Abelian Varieties with Endomorphism Structure -- 10 Abelian Surfaces -- 11 Jacobian Varieties -- 12 Prym Varieties -- A Algebraic Varieties and Complex Analytic Space -- B Line Bundles and Factors of Automorphy -- Bibliograpy -- Glossary of Notation.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-02788-2
Links to Related Works	Subject References: Algebraic Geometry . Mathematics . Number Theory . Authors: author . Birkenhake, Christina . Lange, Herbert. 1943- . Lange, Herbert, 1943- . Corporate Authors: SpringerLink (Online service) . Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics . Classification: 516.35 .

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Complex Abelian Varieties

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