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Complex Abelian Varieties

Name: Complex Abelian Varieties
Brand: Springer, Berlin
SKU: 01651138
Price: 169.09 EUR
Availability: InStock
Author: Christina Birkenhake
ISBN: 9783642058073

Christina Birkenhake

Herbert Lange

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Inglés

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Código Libristo: 01651138

Editores Springer, Berlin, octubre 2010

Abelian varieties are special examples of projective varieties. As such they can be described by a s... Descripción completa

Código Libristo: 01651138

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Abelian varieties are special examples of projective varieties. As such they can be described by a set of homogeneous polynomial equations. The theory of abelian 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.§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.