Singularities of plane curves [EBook] / Eduardo CasasAlvero.
Singularities of plane curves [EBook] / Eduardo CasasAlvero.
This book provides a comprehensive and selfcontained exposition of the algebrogeometric 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...
Personal Name(s):  CasasAlvero, E., (author) 

Imprint: 
Cambridge :
Cambridge University Press,
2000

Physical Description: 
1 online resource (xv, 345 pages) 
Note: 
englisch 
ISBN: 
9780521789592 9780511569326 
Series Title: 
London Mathematical Society lecture note series ;
276 
Subject (LOC):  
Full Text 
Table of 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 yroots of f(x, y)
 The NewtonPuiseux algorithm
 Puiseux theorem
 Separation of yroots
 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.