Authors:
- 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 ?
- Includes supplementary material: sn.pub/extras
Part of the book series: Modern Birkhäuser Classics (MBC)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
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)
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)Authors and Affiliations
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Eitorf, Germany
Egbert Brieskorn
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, Department of Mathematics, ETH Zürich, Zürich, Switzerland
Horst Knörrer
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.
Bibliographic Information
Book Title: Plane Algebraic Curves
Book Subtitle: Translated by John Stillwell
Authors: Egbert Brieskorn, Horst Knörrer
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-3-0348-0493-6
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2012
Softcover ISBN: 978-3-0348-0492-9Published: 26 August 2012
eBook ISBN: 978-3-0348-0493-6Published: 27 August 2012
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: X, 721
Number of Illustrations: 301 b/w illustrations
Additional Information: Originally published 1981 as Ebene algebraische Kurven by Birkhäuser Boston
Topics: Algebraic Geometry, Commutative Rings and Algebras, Algebraic Topology