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.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 DOI:
 10.48550/arXiv.1505.00666
 arXiv:
 arXiv:1505.00666
 Bibcode:
 2015arXiv150500666D
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Commutative Algebra
 EPrint:
 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