Higher Dimensional Varieties and Rational Points (Bolyai Society Mathematical Studies (12)) (English and French Edition)

Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on Higher Dimensional Varieties and Rational Points held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area. "Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on 'Higher Dimensional Varieties and Rational Points' held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area."--Page 4 of cover Front Matter....Pages I-5 Introduction....Pages 7-8 Acknowledgments....Pages 9-9 Front Matter....Pages 11-11 Rational Curves on Varieties....Pages 13-68 Rationally Connected Varieties and Fundamental Groups....Pages 69-92 Fano Varieties....Pages 93-132 Families of Varieties of General Type: the Shafarevich Conjecture and Related Problems....Pages 133-167 Front Matter....Pages 169-169 Points Rationnels sur les Fibrations....Pages 171-221 Potential Density of Rational Points on Algebraic Varieties....Pages 223-282 Fujita’s Program and Rational Points....Pages 283-310