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Higher Dimensional Varieties and Rational Points

  • Book
  • © 2003

Overview

Editors:
  1. Károly Böröczky

    1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

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  2. János Kollár

    1. Department of Mathematics, Princeton University, Princeton, USA

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  3. Tamás Szamuely

    1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

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  • A collection of outstanding articles from the Summer School and Conference on "Higher Dimensional Varieties and Rational Points", Budapest, Sept. 2001
  • Authors include: C. Araujo, J.-L. Colliot-Thélène, O. Debarre, B. Hasset, J. Kollár, S. J. Kovács, Y. Tschinkel
  • The first book to describes the currently emerging interface between higher dimensional birational geometry and the arithmetic of algebraic varieties
  • Presents several new results
  • The first publication to give a complete treatment of several topics that so far existed only in unpublished notes or incomplete versions

Part of the book series: Bolyai Society Mathematical Studies (BSMS, volume 12)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-5
    Download chapter PDF

  2. Introduction

    1. Introduction

      • Károly Böröczky Jr., János Kollár, Tamás Szamuely
      Pages 7-8

  3. Acknowledgments

    1. Acknowledgments

      • Károly Böröczky Jr., János Kollár, Tamás Szamuely
      Pages 9-9

  4. Geometry

    1. Front Matter

      Pages 11-11
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    2. Rational Curves on Varieties

      • Carolina Araujo, János Kollár
      Pages 13-68

    3. Rationally Connected Varieties and Fundamental Groups

      • János Kollár
      Pages 69-92

    4. Fano Varieties

      • Olivier Debarre
      Pages 93-132

    5. Families of Varieties of General Type: the Shafarevich Conjecture and Related Problems

      • Sándor J. Kovács
      Pages 133-167

  5. Arithmetic

    1. Front Matter

      Pages 169-169
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    2. Points Rationnels sur les Fibrations

      • Jean-Louis Colliot-Thélène
      Pages 171-221

    3. Potential Density of Rational Points on Algebraic Varieties

      • Brendan Hassett
      Pages 223-282

    4. Fujita’s Program and Rational Points

      • Yuri Tschinkel
      Pages 283-310
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Keywords

About this book

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. 

Editors and Affiliations

  • Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    Károly Böröczky, Tamás Szamuely

  • Department of Mathematics, Princeton University, Princeton, USA

    János Kollár

Bibliographic Information

  • Book Title: Higher Dimensional Varieties and Rational Points

  • Editors: Károly Böröczky, János Kollár, Tamás Szamuely

  • Series Title: Bolyai Society Mathematical Studies

  • DOI: https://doi.org/10.1007/978-3-662-05123-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2003

  • Hardcover ISBN: 978-3-540-00820-0Published: 10 July 2003

  • Softcover ISBN: 978-3-642-05644-4Published: 15 December 2010

  • eBook ISBN: 978-3-662-05123-8Published: 11 December 2013

  • Series ISSN: 1217-4696

  • Series E-ISSN: 2947-9460

  • Edition Number: 1

  • Number of Pages: II, 310

  • Additional Information: Jointly published with Janos Bolyai Mathematical Society

  • Topics: Algebraic Geometry, Combinatorics, Geometry, Number Theory

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