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

摘要

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