Deformations of plane curves and Jacobian syzygies

2018/08/16 by Dimca, Alexandru, Sticlaru, Gabriel
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.05524

Abstract

We relate the equianalytic and the equisingular deformations of a reduced complex plane curve to the Jacobian syzygies of its defining equation. Several examples and conjectures involving rational cuspidal curves are discussed.

Related

• Plane curves with three syzygies, minimal Tjurina curves curves, and nearly cuspidal curves
• Curves with Jacobian syzygies of the same degree
• Jacobian syzygies and plane curves with maximal global Tjurina numbers
• Syzygies of curves beyond Green's Conjecture
• Free plane curves with a linear Jacobian syzygy