Plane Algebraic Curves: Translated by John Stillwell

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Springer Science & Business Media, 27.08.2012 - 721 Seiten

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)

 

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Inhalt

II INVESTIGATION OF CURVES BY ELEMENTARY ALGEBRAIC METHODS
172
III INVESTIGATION OF CURVES BY RESOLUTION OF SINGULARITIES
323
Bibliography
694
INDEX
702
Urheberrecht

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Über den Autor (2012)

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.

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