The 2-Hessian and sextactic points on plane algebraic curves

• Paul Aleksander Maugesten ^[1] ; Torgunn Karoline Moe ^[1]
  1. [1] University of Oslo

     University of Oslo

     Noruega

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 125, Nº 1, 2019, págs. 13-38
• Idioma: inglés
• DOI: 10.7146/math.scand.a-114715
• Texto completo no disponible (Saber más ...)
• Resumen

  • In an article from 1865, Arthur Cayley claims that given a plane algebraic curve there exists an associated 2-Hessian curve that intersects it in its sextactic points. In this paper we fix an error in Cayley's calculations and provide the correct defining polynomial for the 2-Hessian. In addition, we present a formula for the number of sextactic points on cuspidal curves and tie this formula to the 2-Hessian. Lastly, we consider the special case of rational curves, where the sextactic points appear as zeros of the Wronski determinant of the 2nd Veronese embedding of the curve