Construction of Free Curves by Adding Osculating Conics to a Given Cubic Curve
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.
Authors
- Giovanna Ilardi (ORCID: https://orcid.org/0000-0001-9578-4992)
- Alexandru Dimca (ORCID: https://orcid.org/0000-0001-9679-9870)
- Grzegorz Malara (ORCID: https://orcid.org/0000-0001-5077-4942)
- Piotr Pokora (ORCID: https://orcid.org/0000-0001-8526-9831)
Institutions
- Centre National de la Recherche Scientifique (FR)
- University School of Physical Education in Kraków (PL)
- University of Naples Federico II (IT)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2024-12-30
- DOI
- https://doi.org/10.1093/imrn/rnae273
- Citations
- 2
- Primary Topic
- Advanced Numerical Analysis Techniques
- Type
- article
- Field-Weighted Citation Impact
- 0.75