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<p>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.</p>

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Simplices Osculating Rational Normal Curves

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月16日

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  • Alessio Caminata,
  • Enrico Carlini,
  • Luca Schaffler

摘要

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.