The 0-th Fitting ideal of the Jacobian module of a plane curve

2019/04/16 by Alexandru Dimca, Gabriel Sticlaru, Dimca, Alexandru +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1904.07823

openalex publication_date 2019/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the 0-th Fitting ideal of the Jacobian module of a plane curve in terms of determinants involving the Jacobian syzygies of this curve. This leads to new characterizations of maximal Tjurina curves, that is of non free plane curves, whose global Tjurina number equals an upper bound given by A. du Plessis and C.T.C. Wall.

Related

• Jacobian syzygies and plane curves with maximal global Tjurina numbers
• On the Hilbert vector of the Jacobian module of a plane curve
• Curves with Jacobian syzygies of the same degree
• Jacobian schemes of conic-line arrangements and eigenschemes
• A minimal resolution for the Jacobian ideal of a generic curve arrangement