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

Alexandru DimcaGiovanna IlardiGrzegorz MalaraPiotr Pokora

Nov 2023

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In the present note we construct new families of free and nearly free curves starting from a plane cubic curve $C$ and adding some of its hyperosculating conics. Using obvious group actions, we get new insight into the geometry of the $27$ hyperosculating conics of the Fermat cubic curve.

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