Saturation of Jacobian ideals: Some applications to nearly free curves, line arrangements and rational cuspidal plane curves

Alexandru Dimca (1, 2) , Gabriel Sticlaru (3)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
3 Ovidius University of Constanta

In this note we describe the minimal resolution of the ideal $I_f$, the saturation of the Jacobian ideal of a nearly free plane curve $C:f=0$. In particular, it follows that this ideal $I_f$ can be generated by at most 4 polynomials. Some applications to rational cuspidal plane curves are given, and a natural related question is raised.

Mots clés: Tjurina number; Jacobian ideal; Free curve; Nearly free curve; Rational cuspidal curve

Domaines: Géométrie algébrique [math.AG]; Algèbre commutative [math.AC]

Alexandru Dimca, Gabriel Sticlaru. Saturation of Jacobian ideals: Some applications to nearly free curves, line arrangements and rational cuspidal plane curves. Journal of Pure and Applied Algebra, In press, Journal of Pure and Applied Algebra, ⟨10.1016/j.jpaa.2019.03.009⟩. ⟨hal-01761548⟩