304 research outputs found
A bound for the Milnor number of plane curve singularities
Let be a plane algebraic curve of degree with an isolated
singular point at the origin of the complex plane. We show that the Milnor
number is less than or equal to ,
unless is a set of concurrent lines passing through 0. Then we
characterize the curves for which
Introduction to the local theory of plane algebraic curves
We consider the algebroid plane curves de ned by formal power
series of two variables with coe cients in an algebraically closed eld. Using
quadratic transformations we prove the local normalization theorem. Then we
study the intersection multiplicity of algebroid curves and give an introduction
to the Newton diagrams
Formal and convergent solutions of analytic equations
We provide the detailed proof of a sharpened version of the
M. Artin Approximation Theorem
Invariants of plane curve singularities and Newton diagrams
We present an intersection-theoretical approach to the invariants of plane
curve singularities , , related by the Milnor formula
. Using Newton transformations we give formulae for ,
, which imply planar versions of well-known theorems on
nondegenerate singularities
Euclidean algorithm and polynomial equations after Labatie
We recall Labatie's effective method of solving polynomial equations
with two unknowns by using the Euclidean algorithm
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