Papers › Construction of free curves by adding osculating conics to a given cubic curve

Construction of free curves by adding osculating conics to a given cubic curve

15 Nov 2023arXiv:2311.08913links table onlyarchive 2025-07-28

Alexandru Dimca, Giovanna Ilardi, Grzegorz Malara, Piotr Pokora

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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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