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Curves and Abelian Varieties.
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 boo...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2008.
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| Colección: | Contemporary Mathematics Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Contents; Preface; List of talks; Compactified Jacobians, Abel maps and Theta divisors; 1. Introduction; 2. Compactified Picard schemes; 2.1. Set up; 2.2. Relation between Picard scheme and Néron model; 2.3. Types of Compactified Picard schemes; 2.4. The case d = g â#x80;#x93; 1; 3. Abel maps and Theta divisors; 3.1. Preliminary analysis; 3.2. Abel maps in degree g â#x80;#x93; 1; 3.3. Abel maps of arbitrary degree; 3.4. The theta divisor of Pgâ#x80;#x93;1X; References; Singularities of theta divisors in algebraic geometry; The diagonal property for abelian varieties.
- On isogenous principally polarized abelian surfacesNéron models and boundary components for degenerations of Hodge structure of mirror quintic type; Introduction; Part I: Hodge-theoretic analysis; I.A. Notations and general background; I.B. Integral symplectic linear algebra background; I.C. Analysis of the LMHS in the three cases; Part II. Boundary component structure; II. A. Review of material from [KU]; II. B. Boundary component structure for degenerations of Hodge structure of mirror quintic type; Part III: Geometric setting.
- LII. A Examples of the three cases arising from degenerations of Calabi-Yau threefoldsIII. B Towards motivation of the limiting mixed Hodge structure; Part IV: Frenet framing of complex variations of quintic mirror Hodge structures; 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.