Title Singularities of plane curves / Eduardo Casas-Alvero

Published Cambridge ; New York : Cambridge University Press, 2000

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Description 1 online resource (xv, 345 pages) : illustrations Series London Mathematical Society lecture note series ; 276 London Mathematical Society lecture note series ; 276. Contents Projective spaces -- Power series -- Surfaces, local coordinates -- Morphisms -- Local rings -- Tangent and cotangent spaces -- Curves -- Germs of curves -- Multiplicity and tangent cone -- Smooth germs -- Examples of singular germs -- Newton--Puiseux algorithm -- Newton polygon -- Fractionary power series -- Search for y-roots of f(x, y) -- The Newton-Puiseux algorithm -- Puiseux theorem -- Separation of y-roots -- The case of convergent series -- Algebraic properties of C{x, y} -- First local properties of plane curves -- The branches of a germ -- The Puiseux series of a germ -- Points on curves around O -- Local rings of germs -- Parameterizing branches -- Intersection multiplicity -- Pencils and linear systems -- Infinitely near points -- Blowing up -- Transforming curves and germs -- Infinitely near points -- Enriques' definition of infinitely near points -- Proximity -- Free and satellite points -- Resolution of singularities -- Equisingularity -- Enriques diagrams -- The ring in the first neighbourhood -- The rings in the successive neighbourhoods -- Artin theorem for plane curves -- Virtual multiplicities -- Curves through a weighted cluster -- When virtual multiplicities are effective -- Blowing up all points in a cluster -- Exceptional divisors and dual graphs -- The totla transform of a curve -- Unloading -- The number of conditions -- Adjoint germs and curves -- Noether's Af + B[phi] theorem -- Analysis of branches -- Characteristic exponents -- The first characteristic exponent Summary Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results Bibliography Includes bibliographical references (pages 333-338) and index Notes Print version record Subject Curves, Plane. Singularities (Mathematics) MATHEMATICS -- Geometry -- Algebraic. Curves, Plane Singularities (Mathematics) Manifolds. Krommen. Singulariteiten. Courbes planes. Singularités (Mathématiques) Form Electronic book ISBN 9781107363113 110736311X 9780511569326 0511569327 9781107368026 1107368022

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