Singularities of Plane Curves

Eduardo Casas-Alvero (Universitat de Barcelona), N. J. Hitchin

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English

Cambridge University Press
15 October 2000

Analytic geometry

Series: London Mathematical Society Lecture Note Series

This book provides a comprehensive and self-contained exposition of the algebro-geometric theory of singularities of plane curves, covering both its classical and its modern aspects. The book gives a unified treatment, with complete proofs, presenting modern results which have only ever appeared in research papers. It updates and correctly proves a number of important classical results for which there was formerly no suitable reference, and includes new, previously unpublished results as well as applications to algebra and algebraic geometry.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, or as a supplementary text for courses on algebraic geometry (algebraic curves) or commutative algebra (valuations, complete ideals).

By: Eduardo Casas-Alvero (Universitat de Barcelona)
Series edited by: N. J. Hitchin
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 276
Dimensions: Height: 228mm, Width: 154mm, Spine: 22mm
Weight: 520g
ISBN: 9780521789592
ISBN 10: 0521789591
Series: London Mathematical Society Lecture Note Series
Pages: 364
Publication Date: 15 October 2000
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.