Rational Points, Rational Curves, and Entire Holomorphic Curves on Projective Varieties
This volume contains papers from the Short Thematic Program on Rational Points, Rational Curves, and Entire Holomorphic Curves and Algebraic Varieties, held from June 3-28, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Québec, Canada. The program was dedicated to the study...
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| Main Authors: | , , , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
22.12.2015
Centre de Recherches Mathematiques |
| Edition: | 1 |
| Series: | Contemporary Mathematics |
| Subjects: | |
| ISBN: | 1470414589, 9781470414580 |
| ISSN: | 0271-4132, 1098-3627 |
| Online Access: | Get full text |
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Table of Contents:
- Expository and survey articles -- Some applications of <inline-formula content-type="math/mathml"> p p </inline-formula>-adic uniformization to algebraic dynamics -- Special manifolds, arithmetic and hyperbolic aspects: a short survey -- Invitation to integral and rational points on curves and surfaces -- Roth’s theorem: an introduction to diophantine approximation -- The Thue-Siegel method in diophantine geometry -- Research articles -- Optimal pinching for the holomorphic sectional curvature of Hitchin’s metrics on Hirzebruch surfaces -- The Lefschetz property for families of curves -- Separable rational connectedness and stability -- Curve classes on rationally connected varieties
- 2. Basic definitions and description of the family of metrics under consideration -- 3. Proof of Theorem 1.1 -- 4. Geometric interpretation of our computations -- 5. Proof of Theorem 1.2 -- References -- The Lefschetz property for families of curves -- References -- Separable rational connectedness and stability -- References -- Curve classes on rationally connected varieties -- 1. Introduction -- 2. Preliminaries -- 3. Proof of the Main Theorem -- References -- Back Cover
- Cover -- Title page -- Contents -- Preface -- Expository and survey articles -- Some applications of -adic uniformization to algebraic dynamics -- 1. A motivation: potential density -- 2. Near a fixed point -- 3. Uniformization of orbits and applications -- 4. Acknowledgments -- References -- Special manifolds, arithmetic and hyperbolic aspects: a short survey -- 1. Introduction -- 2. Special manifolds: Bogomolov sheaves -- 3. Special manifolds: orbifold base -- 4. The orbifold version ^{ }_{ , } of the _{ , } conjecture -- 5. The core fibration -- 6. The decomposition =( )ⁿ of the core -- 7. Conjectures for smooth and integral orbifolds -- 8. Examples of fibrations of general type on simply-connected manifolds -- 9. Orbifold cotangent sheaves: generic semi-positivity, applications -- 10. H-principle and specialness -- References -- Invitation to integral and rational points on curves and surfaces -- 1. Introduction -- 2. Some Diophantine equations -- 3. Diophantine geometry - rational and integral points on curves -- 4. Rational and integral points on surfaces -- References -- Roth's theorem: an introduction to diophantine approximation -- 0. Introduction -- 1. Liouville's theorem and beyond -- 2. Roth's theorem: an overview -- 3. Controlling the index: Roth's lemma -- 4. Controlling the index: Dyson's lemma -- 5. Extensions and questions -- References -- The Thue-Siegel method in diophantine geometry -- 1. The Thue-Siegel method -- 2. Basic constructions in Bombieri's proof -- 3. Divisors, heights, and Jacobians -- 4. An upper bound for the height -- 5. A lower bound -- 6. Construction of a global section -- 7. The index -- 8. The end of the proof -- References -- Research articles -- Optimal pinching for the holomorphic sectional curvature of Hitchin's metrics on Hirzebruch surfaces -- 1. Introduction