Singularities of Plane Curves

by Eduardo Casas-Alvero

Overview

This comprehensive and self-contained exposition of the algebro-geometric theory of singularities of plane curves covers both the classical and modern aspects of the field. It gives a unified treatment with complete proofs and presents modern results which have only appeared in research papers. It updates and correctly proves a number of important classical results for which there was formerly no suitable reference. With new, previously unpublished results as well as applications to algebra and algebraic geometry, this book will be useful as a reference text for researchers in the field. It is also suitable as a textbook for postgraduate courses on singularities.

Product Details

ISBN-13:	9780521789592
Publisher:	Cambridge University Press
Publication date:	08/31/2000
Series:	London Mathematical Society Lecture Note Series , #276
Pages:	364
Product dimensions:	6.06(w) x 8.98(h) x 0.87(d)

Table of Contents

Preface; Preliminaries; 1. Newton-Puiseux algorithm; 2. First local properties of plane curves; 3. Infinitely near points; 4. Virtual multiplicities; 5. Analysis of branches; 6. Polar germs and related invariants; 7. Linear families of germs; 8. Valuations and complete ideals; A. Applications to affine geometry.

Editorial Reviews

"I like this book very much. The monograph offers a complete easy reading on singularities of complex plane curves and I think it is a very useful text for a postgraduate course in the subject." Mathematical Reviews

From the Publisher

Casas-Alvero (U. of Barcelona) offers researchers a self-contained exposition of the algebro-geometric theory of singularities of plane curves, considering both its classical and modern aspects. In addition to presenting complete proofs and results that have appeared in recent research papers, he also updates and correctly proves a number of classical results for which there was previously no suitable reference. His work could also be used as a textbook for a graduate course on singularities or a supplement for courses on algebraic geometry or commutative algebra, and includes exercises to that end. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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