Modern Birkhäuser Classics

Plane Algebraic Curves

Translated by John Stillwell

Authors: Brieskorn, Egbert, Knörrer, Horst

  • Lively introduction and overview of the field
  • Anchors the subject in history, science and technology
  • Clearly explains the tools from local analytic geometry and from algebraic and differential topology
  • Presents a wealth of attractive geometric illustrations ​
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About this book

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 a 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 authorsʼ concern for the student audience through its emphasis on motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles. This text also 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)

About the authors

Egbert Brieskorn was a Professor of Mathematics at the University of Bonn, Germany.

Horst Knörrer is a Professor of Mathematics at the ETH Zurich, Switzerland.

Reviews

“It provides a comprehensive overview for all who are interested in GO with an emphasis on theory and algorithms.” (W. Huyer, Monatshefte für Mathematik, 2015)

“This is a masterly expositional work in which the conversational style of narrative never leaves the reader in doubt about the direction of enquiry. … the richness of this publication really resides in the fascinating range of mathematical ideas that support its main line of enquiry. … it can be read selectively at so many different levels up to the postgraduate stage.” (PeterRuane,The Mathematical Association of America, January, 2013)

Table of contents (9 chapters)

  • I History of algebraic curves

    Brieskorn, Egbert (et al.)

    Pages 1-65

  • 2. Synthetic and analytic geometry

    Brieskorn, Egbert (et al.)

    Pages 66-101

  • 3. The development of projective geometry

    Brieskorn, Egbert (et al.)

    Pages 102-171

  • II Investigation of curves by elementary algebraic methods

    Brieskorn, Egbert (et al.)

    Pages 172-201

  • 5. Definition and elementary properties of plane algebraic curves

    Brieskorn, Egbert (et al.)

    Pages 202-226

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0348-0493-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-0348-0492-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Plane Algebraic Curves
Book Subtitle
Translated by John Stillwell
Authors
Translated by
Stillwell, J.
Series Title
Modern Birkhäuser Classics
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0493-6
DOI
10.1007/978-3-0348-0493-6
Softcover ISBN
978-3-0348-0492-9
Series ISSN
2197-1803
Edition Number
1
Number of Pages
X, 721
Number of Illustrations and Tables
301 b/w illustrations
Additional Information
Originally published 1981 as Ebene algebraische Kurven by Birkhäuser Boston
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