Moduli of Abelian Varieties
Adler, Allan.
Moduli of Abelian Varieties [electronic resource] / by Allan Adler, Sundararaman Ramanan. - VI, 202 p. online resource. - Lecture Notes in Mathematics, 1644 0075-8434 ; . - Lecture Notes in Mathematics, 1644 .
Standard Heisenberg Groups -- Heisenberg groups of line bundles on abelian varieties -- Theta structures and the addition formula -- Geometry and arithmetic of the fundamental relations -- Invariant theory, arithmetic and vector bundles.
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.
9783540496090
10.1007/BFb0093659 doi
Geometry, algebraic.
Number theory.
Algebraic Geometry.
Number Theory.
QA564-609
516.35
Moduli of Abelian Varieties [electronic resource] / by Allan Adler, Sundararaman Ramanan. - VI, 202 p. online resource. - Lecture Notes in Mathematics, 1644 0075-8434 ; . - Lecture Notes in Mathematics, 1644 .
Standard Heisenberg Groups -- Heisenberg groups of line bundles on abelian varieties -- Theta structures and the addition formula -- Geometry and arithmetic of the fundamental relations -- Invariant theory, arithmetic and vector bundles.
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.
9783540496090
10.1007/BFb0093659 doi
Geometry, algebraic.
Number theory.
Algebraic Geometry.
Number Theory.
QA564-609
516.35