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Plane Algebraic Curves

Plane Algebraic Curves
Catalogue Information
Field name Details
Dewey Class 516.35
Title Plane Algebraic Curves (EB) / Egbert Brieskorn, Horst Knörrer ; translated by John Stillwell.
Author Brieskorn, Egbert
Added Personal Name Knörrer, Horst
Other name(s) SpringerLink (Online service)
Publication Basel : Birkhäuser
, 2012.
Physical Details X, 721 p. 301 illus. : online resource.
Series Modern Birkhauser classics
ISBN 9783034804936
Summary Note 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, âPlane Algebraic Curvesâ reflects the authorâs 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.   ---   In the first chapter one finds many special curves with very attractive geometric presentations â the wealth of illustrations is a distinctive characteristic of this book â and an introduction to projective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezoutâs theorem and a detailed discussion of cubics. The heart of this book â and how else could it be with the first author â is the chapter on the resolution of singularities (always over the complex numbers).  (â¦) 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):
Contents note I. History of algebraic curves -- 1. Origin and generation of curves -- 2. Synthetic and analytic geometry -- 3. The development of projective geometry -- II. Investigation of curves by elementary algebraic methods -- 4. Polynomials -- 5. Definition and elementary properties of plane algebraic curves -- 6. The intersection of plane curves -- 7. Some simple types of curves -- III. Investigation of curves by resolution of singularities -- 8. Local investigations -- 9. Global investigations -- Bibliography -- Index.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site http://dx.doi.org/10.1007/978-3-0348-0493-6
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