Effective construction of irreducible curve singularities
Algebraic Geometry
2007-05-23 v1 Commutative Algebra
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.
Cite
@article{arxiv.math/0507135,
title = {Effective construction of irreducible curve singularities},
author = {Abdallah Assi and Margherita Barile},
journal= {arXiv preprint arXiv:math/0507135},
year = {2007}
}
Comments
20 pages, Latex