On the Saito basis for plane curves

2025/05/24 by Emilio Carvalho, de Carvalho, Emilio, Percy Fernández-Sánchez +3
Computer Science · Engineering · #14H20 #32S10 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2505.18868

openalex publication_date 2025/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present some results concerning the Saito module and the torsion submodule of an analytic plane curve, and we provide a method for computing them. Using this algorithm, we compute analytic invariants for plane curves with multiplicity less than or equal to three.

Citations

• The Tjurina number of a plane curve with two branches and high intersection multiplicity
• Colengths of fractional ideals and Tjurina number of a reducible plane curve
• On the Saito number of plane curves
• Computing a Saito basis from a standard basis
• Tjurina number of a local complete intersection curve
• On the Saito's basis and the Tjurina Number for Plane Branches
• Standard Bases for Fractional Ideals of the Local Ring of an Algebroid\n Curve

Related

• Computing a Saito basis from a standard basis
• On the Saito number of plane curves
• On the Saito's basis and the Tjurina Number for Plane Branches
• The Saito vector field of a germ of complex plane curve
• The Saito module and the moduli of a germ of curve in (ℂ²,0)