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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number of important classical results for which there was formerly no suitable reference, and includes new, previously unpublished results as well as applications to algebra and algebraic geometry.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).
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.
A comprehensive and self-contained exposition of the algebro-geometric theory of singularities of plane curves, covering both its classical and its modern aspects and presenting new, previously unpublished results. This book will be useful as a reference text for researchers and is also suitable as a textbook for postgraduate courses.
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
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.
A comprehensive and self-contained exposition of the algebro-geometric theory of singularities of plane curves, covering both its classical and its modern aspects and presenting new, previously unpublished results. This book will be useful as a reference text for researchers and is also suitable as a textbook for postgraduate courses.
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.