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Effective construction of irreducible curve singularities

Abdallah Assi·Margherita Barile
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Abstract

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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Abdallah Assi, Margherita Barile. 2005-07-07. Effective construction of irreducible curve singularities. https://arxiv.org/abs/math/0507135

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