TY  - BOOK
AU  - Casas-Alvero,E.
TI  - Singularities of plane curvesEduardo Casas-Alvero
T2  - London Mathematical Society lecture note series
SN  - 9781107363113
AV  - QA565 .S564 2000
PY  - 2000///
CY  - Cambridge, New York
PB  - Cambridge University Press
KW  - Curves, Plane
KW  - Singularities (Mathematics)
KW  - Electronic Books
N1  - 2; 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; 2; b
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