Curves and Abelian Varieties
About this Volume
Edited by: Valery Alexeev, Arnaud Beauville, C. Herbert Clemens and Elham Izadi
2008: Volume: 465
ISBNs: 978-0-8218-4334-5 (print); 978-0-8218-8144-6 (online)
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.
Graduate students and research mathematicians interested in algebraic geometry.
Table of Contents
- Lucia Caporaso – Compactified Jacobians, Abel maps and theta divisors
- Sebastian Casalaina-Martin – Singularities of theta divisors in algebraic geometry
- Olivier Debarre – The diagonal property for abelian varieties
- I. Dolgachev and D. Lehavi – On isogenous principally polarized abelian surfaces
- Mark Green, Phillip Griffiths and Matt Kerr – Néron models and boundary components for degenerations of Hodge structure of mirror quintic type
- V. Kanev and H. Lange – Polarization type of isogenous Prym-Tyurin varieties
- Alina Marian and Dragos Oprea – A tour of theta dualities on moduli spaces of sheaves
- Grigory Mikhalkin and Ilia Zharkov – Tropical curves, their Jacobians and theta functions
- Martin Olsson – Logarithmic interpretation of the main component in toric Hilbert schemes
- Alessandro Verra – On the universal principally polarized abelian variety of dimension 4