Rational Points, Rational Curves, and Entire Holomorphic Curves on Projective Varieties
About this Title
Carlo Gasbarri, Université de Strasbourg, Strastourg, France, Steven Lu, Université du Québec à Montréal, Montréal, Québec, Canada, Mike Roth, Queen’s University, Kingston, Ontario, Canada and Yuri Tschinkel, Courant Institute of Mathematical Sciences, New York, NY, Editors
Publication: Contemporary Mathematics
Publication Year 2015: Volume 654
ISBNs: 978-1-4704-1458-0 (print); 978-1-4704-2841-9 (online)
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.
Graduate students and research mathematicians interested in Diophantine/arithmetic geometry, special varieties, and geometry of rational/holomorphic curves.
Table of Contents
- Ekaterina Amerik – Some applications of $p$-adic uniformization to algebraic dynamics
- Frédéric Campana – Special manifolds, arithmetic and hyperbolic aspects: a short survey
- Pranabesh Das and Amos Turchet – Invitation to integral and rational points on curves and surfaces
- Michael Nakamaye – Roth’s theorem: an introduction to diophantine approximation
- Paul Vojta – The Thue-Siegel method in diophantine geometry
- Angelynn Alvarez, Ananya Chaturvedi and Gordon Heier – Optimal pinching for the holomorphic sectional curvature of Hitchin’s metrics on Hirzebruch surfaces
- János Kollár – The Lefschetz property for families of curves
- Zhiyu Tian – Separable rational connectedness and stability
- Runhong Zong – Curve classes on rationally connected varieties