Nearly free divisors and rational cuspidal curves
Alexandru Dimca, Gabriel Sticlaru
TL;DR
This paper introduces a new class of plane curves near free divisors, conjecturally including all rational cuspidal curves, and proves that unicuspidal rational curves with one Puiseux pair are either free or in this class.
Contribution
It defines a new class of curves close to free divisors and proves a key property relating unicuspidal rational curves to this class.
Findings
Unicuspidal rational curves with one Puiseux pair are either free or belong to the new class.
The new class potentially contains all rational cuspidal curves.
The paper connects recent results to the classification of special plane 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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Advanced Combinatorial Mathematics