Plane Algebraic Curves

Translated by John Stillwell

  • Egbert Brieskorn
  • Horst Knörrer

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-x
  2. Egbert Brieskorn, Horst Knörrer
    Pages 1-65
  3. Egbert Brieskorn, Horst Knörrer
    Pages 66-101
  4. Egbert Brieskorn, Horst Knörrer
    Pages 102-171
  5. Egbert Brieskorn, Horst Knörrer
    Pages 172-201
  6. Egbert Brieskorn, Horst Knörrer
    Pages 202-226
  7. Egbert Brieskorn, Horst Knörrer
    Pages 227-277
  8. Egbert Brieskorn, Horst Knörrer
    Pages 278-322
  9. Egbert Brieskorn, Horst Knörrer
    Pages 323-575
  10. Egbert Brieskorn, Horst Knörrer
    Pages 576-693
  11. Back Matter
    Pages 694-721

About this book

Introduction

In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, “Plane Algebraic Curves” reflects the author’s concern for the student audience through emphasis upon motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles; this text provides a foundation for the comprehension and exploration of modern work on singularities.  

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In the first chapter one finds many special curves with very attractive geometric presentations – the wealth of illustrations is a distinctive characteristic of this book – and an introduction to projective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezout’s theorem and a detailed discussion of cubics. The heart of this book – and how else could it be with the first author – is the chapter on the resolution of singularities (always over the complex numbers).  (…) Especially remarkable is the outlook to further work on the topics discussed, with numerous references to the literature. Many examples round off this successful representation of a classical and yet still very much alive subject.

(Mathematical Reviews)

Keywords

Bézout's theorem algebraic geometry analytic geometry projective geometry resolution of singularities

Authors and affiliations

  • Egbert Brieskorn
    • 1
  • Horst Knörrer
    • 2
  1. 1.EitorfGermany
  2. 2., Department of MathematicsETH ZürichZürichSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0493-6
  • Copyright Information Springer Basel 2012
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0492-9
  • Online ISBN 978-3-0348-0493-6
  • About this book