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Construction of Free Curves by Adding Osculating Conics to a Given Cubic Curve

Year: 2024
Type: article
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.
DOI: 10.1093/imrn/rnae273
Institutions: Centre National de la Recherche Scientifique, Université Côte d'Azur, Laboratoire Jean-Alexandre Dieudonné, IMAR - Institutul de Matematică „Simion Stoilow” al Academiei Române, University of Naples Federico II, Uniwersytet Komisji Edukacji Narodowej w Krakowie
Language: English
Open Access status: hybrid
Estimated APC paid: $4,534
OpenAlex ID: W4405905367
FWCI: 1.346
Cites: 14
Cited by: 2
Related to: 10