2005/07/07 by Abdallah Assi, Assi, Abdallah, Margherita Barile +1
Computer Science · Engineering · Mathematics · #32S15 #68W30 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:32S15 #msc:68W30
paper · pdf · doi:10.48550/arxiv.math/0507135
20 pages, Latex
arxiv created 2005/07/07 · openalex publication_date 2005/07/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.