Singularities of plane curvesEduardo Casas-Alvero.
Casas-Alvero, E. 1948-
Singularities of plane curvesEduardo Casas-Alvero. - Cambridge ; New York : Cambridge University Press, (c)2000. - 1 online resource (xv, 345 pages) : illustrations. - London Mathematical Society lecture note series ; 276 .
Includes bibliographies and index.
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 -- 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.
9781107363113
Curves, Plane.
Singularities (Mathematics)
Electronic Books.
QA565 / .S564 2000
Singularities of plane curvesEduardo Casas-Alvero. - Cambridge ; New York : Cambridge University Press, (c)2000. - 1 online resource (xv, 345 pages) : illustrations. - London Mathematical Society lecture note series ; 276 .
Includes bibliographies and index.
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 -- 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.
9781107363113
Curves, Plane.
Singularities (Mathematics)
Electronic Books.
QA565 / .S564 2000