Nearly free divisors and rational cuspidal curves

Abstract

We define a class of plane curves which are close to the free divisors and such that conjecturally it contains the class of rational cuspidal curves. Using a recent result by U. Walther we show that any unicuspidal rational curve with a unique Puiseux pair is either free or belongs to this class.

v3: title modified and the topological results strengthened. In particular, any rational cuspidal curve whose degree is either even or a prime power, or which has an abelian group, is a nearly free divisor