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Higher Dimensional Varieties and Rational Points

✍ Scribed by Károly Böröczky Jr., János Kollár, Tamás Szamuely (auth.), Károly Böröczky Jr., János Kollár, Tamás Szamuely (eds.)

Publisher
Springer-Verlag Berlin Heidelberg
Year
2003
Leaves
307
Series
Bolyai Society Mathematical Studies 12
Edition
1
Category
Library
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✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Combinatorics; Algebraic Geometry; Geometry; Number Theory

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