**Contemporary Mathematics**

Volume: 654;
2015;
165 pp;
Softcover

MSC: Primary 11; 14; 37;

Print ISBN: 978-1-4704-1458-0

Product Code: CONM/654

List Price: $105.00

Individual Member Price: $84.00

**Electronic ISBN: 978-1-4704-2841-9
Product Code: CONM/654.E**

List Price: $105.00

Individual Member Price: $84.00

# Rational Points, Rational Curves, and Entire Holomorphic Curves on Projective Varieties

Share this page *Edited by *
*Carlo Gasbarri; Steven Lu; Mike Roth; Yuri Tschinkel*

A co-publication of the AMS and Centre de Recherches Mathématiques

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 of subtle interconnections between geometric and arithmetic properties of higher-dimensional algebraic varieties. The main areas of the program were, among others, proving density of rational points in Zariski or analytic topology on special varieties, understanding global geometric properties of rationally connected varieties, as well as connections between geometry and algebraic dynamics exploring new geometric techniques in Diophantine approximation.

#### Table of Contents

# Table of Contents

## Rational Points, Rational Curves, and Entire Holomorphic Curves on Projective Varieties

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- Expository and survey articles 110 free
- Some applications of 𝑝-adic uniformization to algebraic dynamics 312
- Special manifolds, arithmetic and hyperbolic aspects: a short survey 2332
- 1. Introduction 2332
- 2. Special manifolds: Bogomolov sheaves 2433
- 3. Special manifolds: orbifold base 2837
- 4. The orbifold version 𝐶^{𝑜𝑟𝑏}_{𝑛,𝑚} of the 𝐶_{𝑛,𝑚} conjecture 3140
- 5. The core fibration 3241
- 6. The decomposition 𝑐=(𝐽𝑟)ⁿ of the core 3443
- 7. Conjectures for smooth and integral orbifolds 4049
- 8. Examples of fibrations of general type on simply-connected manifolds 4554
- 9. Orbifold cotangent sheaves: generic semi-positivity, applications 4655
- 10. H-principle and specialness 4958
- References 5059

- Invitation to integral and rational points on curves and surfaces 5362
- Roth’s theorem: an introduction to diophantine approximation 7584
- The Thue-Siegel method in diophantine geometry 109118
- 1. The Thue-Siegel method 111120
- 2. Basic constructions in Bombieri’s proof 116125
- 3. Divisors, heights, and Jacobians 117126
- 4. An upper bound for the height 119128
- 5. A lower bound 120129
- 6. Construction of a global section 123132
- 7. The index 125134
- 8. The end of the proof 126135
- References 128137

- Research articles 131140
- Optimal pinching for the holomorphic sectional curvature of Hitchin’s metrics on Hirzebruch surfaces 133142
- The Lefschetz property for families of curves 143152
- Separable rational connectedness and stability 155164
- Curve classes on rationally connected varieties 161170
- Back Cover Back Cover1176

#### Readership

Graduate students and research mathematicians interested in Diophantine/arithmetic geometry, special varieties, and geometry of rational/holomorphic curves.