By Alexandru Dimca and others

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.

November 15, 2023

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

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