Moduli of Abelian Varieties

Allan Adler, Sundararaman Ramanan (auth.)3540620230, 9783540620235

This is a book aimed at researchers and advanced graduate students in algebraic geometry, interested in learning about a promising direction of research in algebraic geometry. It begins with a generalization of parts of Mumford’s theory of the equations defining abelian varieties and moduli spaces. It shows through striking examples how one can use these apparently intractable systems of equations to obtain satisfying insights into the geometry and arithmetic of these varieties. It also introduces the reader to some aspects of the research of the first author into representation theory and invariant theory and their applications to these geometrical questions.

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Table of contents :
Introduction….Pages 1-7
Standard Heisenberg Groups….Pages 8-17
Heisenberg groups of line bundles on abelian varieties….Pages 18-30
Theta structures and the addition formula….Pages 31-51
Geometry and arithmetic of the fundamental relations….Pages 52-76
Invariant theory, arithmetic and vector bundles….Pages 77-106