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

Abstract

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. Related general results by Hassanzadeh and Simis on the saturation of codimension 2 ideals are discussed in detail. Some applications to rational cuspidal plane curves and to line arrangements are also given.

v3: minor changes, final version

References in corpus (3)

• Nearly free divisors and rational cuspidal curves
• On the splitting types of bundles of logarithmic vector fields along plane curves
• Combinatorics of line arrangements and dynamics of polynomial vector fields