Singularities of Plane Curves

ISBN-13: 9780521789592 / Angielski / Miękka / 2000 / 364 str.

E. Casas-Alvero; Eduardo Casas-Alvero; N. J. Hitchin

Opis

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 With new, previously unpublished results as well as applications to algebra and algebraic geometry, this book will be useful as a reference text for researchers in the field.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.

Recenzje

'… it belongs on the shelf of every mathematician interested in curves and their singularities.' K. H. Kiyek, Zentralblatt für Mathematik

Spis treści

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.