We define a class of plane curves that are close to the free divisors in terms of the local cohomology of their Jacobian algebras and such that, conjecturally, any rational cuspidal curve is either free or belongs to this class. We prove this conjecture when the degree of is either even or a prime power, or when the group of is abelian.
Cite this article
Alexandru Dimca, Gabriel Sticlaru, Free and Nearly Free Curves vs. Rational Cuspidal Plane Curves. Publ. Res. Inst. Math. Sci. 54 (2018), no. 1, pp. 163–179DOI 10.4171/PRIMS/54-1-6