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 If, the saturation of the Jacobian ideal of a nearly free plane curve C:f=0. In particular, it follows that this ideal If 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.