Effective construction of irreducible curve singularities

Details Effective construction of irreducible curve singularities Effective construction of irreducible curve singularities

2005-07-07

arxiv.org/abs/math/0507135v1

Mathematics

Algebraic Geometry

20 pages, Latex

Scientific paper

We can associate with any irreducible curve singularity (ics) a numerical semigroup. Two ics are said to be equisingular if they have the same semigroup. Two equisingular ics have the same Milnor number. Conversely, The set of ics with a given Milnor number is a union of equisingular classes. Here we study ics from an algorithmic viewpoint, by using the notion of approximate roots. We give two algorithms: the first one constructs the canonical equation of a curve with a given semigroup. The second one gives the set of semigroups with a fixed Milnor number. The paper is backed by Maple and Mathematica programs which are available upon request.

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