Key points are not available for this paper at this time.
The goal of this paper is to establish a new and efficient characterization of quasi-homogeneous isolated singularities of free curves and nearly free curves C in P². The criterion will be in terms of the first syzygy matrix associated with the Jacobian ideal of f where f=0 is the equation of the plane curve C.
Andrade et al. (Mon,) studied this question.