This book is devoted to recent progress in the study of curves and abelian varieties. It discusses both classical aspects of this deep and beautiful subject as well as two important new developments, tropical geometry and the theory of log schemes. In addition to original research articles, this book contains three surveys devoted to singularities of theta divisors, of compactified Jacobians of singular curves, and of ""strange duality"" among moduli spaces of vector bundles on algebraic varieties.
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Für höhere Schule und Studium
Für Beruf und Forschung
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ISBN-13
978-0-8218-4334-5 (9780821843345)
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Schweitzer Klassifikation
Herausgeber*in
University of Georgia, Athens, GA
Universite de Nice, Cedex, France
Ohio State University, Columbus, OH
University of Georgia, Athens, GA
Compactified Jacobians, Abel maps and theta divisors; Singularities of theta divisors in algebraic geometry; The diagonal property for abelian varieties; On isogenous principally polarized abelian surfaces; Neron models and boundary components for degenerations of Hodge structure of mirror quintic type; Polarization type of isogenous Prym-Tyurin varieties; A tour of theta dualities on moduli spaces of sheaves; Tropical curves, their Jacobians and theta functions; Logarithmic interpretation of the main component in toric Hilbert schemes; On the universal principally polarized abelian variety of dimension 4
