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Integral Points on Algebraic Varieties

An Introduction to Diophantine Geometry

  • Book
  • © 2016

Overview

Authors:
  1. Pietro Corvaja

    1. Dipartimento di Matematica, Università degli studi di Udine, Udine, Italy

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  • Introduces problems in Diophantine geometry and their recent results
  • Investigates the distribution of integral points on algebraic varieties
  • Discusses about the Siegel’s finiteness theorem for integral points on curves

Part of the book series: HBA Lecture Notes in Mathematics (HBALNM)

Part of the book sub series: IMSc Lecture Notes in Mathematics (IMSLNM)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
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  2. Integral points on algebraic varieties

    • Pietro Corvaja
    Pages 1-18

  3. Diophantine approximation

    • Pietro Corvaja
    Pages 19-30

  4. The theorems of Thue and Siegel

    • Pietro Corvaja
    Pages 31-43

  5. Hilbert Irreducibility Theorem

    • Pietro Corvaja
    Pages 45-54

  6. Integral points on surfaces

    • Pietro Corvaja
    Pages 55-71

  7. Back Matter

    Pages 73-75
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Keywords

About this book

This book is intended to be an introduction to Diophantine geometry. The central theme of the book is to investigate the distribution of integral points on algebraic varieties. This text rapidly introduces problems in Diophantine geometry, especially those involving integral points, assuming a geometrical perspective. It presents recent results not available in textbooks and also new viewpoints on classical material. In some instances, proofs have been replaced by a detailed analysis of particular cases, referring to the quoted papers for complete proofs. A central role is played by Siegel’s finiteness theorem for integral points on curves. The book ends with the analysis of integral points on surfaces.

Authors and Affiliations

  • Dipartimento di Matematica, Università degli studi di Udine, Udine, Italy

    Pietro Corvaja

About the author

Pietro Corvaja is full professor of geometry at the Dipartimento Di Mathematica Einformatica at the Universita’ degli studi di udine, Italy. His research topics are arithmetic geometry, Diophantine approximation and the theory of transcendental numbers.

Bibliographic Information

  • Book Title: Integral Points on Algebraic Varieties

  • Book Subtitle: An Introduction to Diophantine Geometry

  • Authors: Pietro Corvaja

  • Series Title: HBA Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-981-10-2648-5

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media Singapore 2016 and Hindustan Book Agency 2016 2016

  • eBook ISBN: 978-981-10-2648-5Published: 23 November 2016

  • Series ISSN: 2509-8063

  • Series E-ISSN: 2509-8071

  • Edition Number: 1

  • Number of Pages: IX, 75

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Algebra, Integral Equations, Geometry

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