2023•arXiv (Cornell University)Open access
Construction of free curves by adding osculating conics to a given cubic curve
Alexandru Dimca, Giovanna Ilardi, Grzegorz Malara, Piotr Pokora
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Abstract
In the present article we construct new families of free and nearly free curves starting from a plane cubic curve $C$ 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 $27$ hyperosculating conics of the Fermat cubic curve using well-chosen group actions.
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