Simplices Osculating Rational Normal Curves
Abstract A classical result of von Staudt states that if eight planes osculate a twisted cubic curve and we divide them into two groups of four, then the eight vertices of the corresponding tetrahedra lie on a twisted cubic curve. In the current paper, we give an alternative proof of this result using modern tools, and at the same time we prove the analogous result for rational normal curves in any projective space. This higher dimensional generalization was claimed without proof in a paper of H.S. White in 1921.
Authors
- Alessio Caminata (ORCID: https://orcid.org/0000-0001-5227-807X)
- Luca Schaffler (ORCID: https://orcid.org/0000-0002-1496-7795)
- Enrico Carlini (ORCID: https://orcid.org/0000-0003-4091-2867)
Institutions
- Roma Tre University (IT)
- Politecnico di Torino (IT)
- Istituto Nazionale di Fisica Nucleare, Sezione di Genova (IT)
- University of Genoa (IT)
Publication Details
- Journal
- Vietnam Journal of Mathematics
- Published
- 2025-04-16
- DOI
- https://doi.org/10.1007/s10013-025-00737-y
- Primary Topic
- Polynomial and algebraic computation
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Università degli Studi Roma Tre
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- European Commission
- Universitat de Barcelona
- Ministero dell'Università e della Ricerca
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni