Construction of free curves by adding osculating conics to a given cubic curve
arXiv:2311.08913 · doi:10.1093/imrn/rnae273
Abstract
In the present article we construct new families of free and nearly free curves starting from a plane cubic curve and adding some of its hyperosculating conics. We present results that involve nodal cubic curves and the Fermat cubic. In addition, we provide new insight into the geometry of the hyperosculating conics of the Fermat cubic curve using well-chosen group actions.
14 pages, final version incorporating referee's remarks, to appear in International Mathematical Research Notes