On the Jacobian Scheme of a plane curve

2023/02/14 by Stefano Canino, Canino, Stefano, Alessandro Gimigliano +3 · 1 citation
Computer Science · Mathematics · #14B05 #14H20 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2302.07042

openalex publication_date 2023/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Jacobian scheme of a plane algebraic curve at an ordinary singularity, characterizing it through a geometric property. We compute the Tjurina number for a family of curves at an ordinary singularity showing that it reaches the minimum possible value, using very elementary methods, essentially Gröbner basis. We give an algorithm that gives the analytic type of a double point using the algebraic version of the Mather-Yau Theorem.

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• Postulation of schemes of length at most 4 on surfaces

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