The $2$-Hessian and sextactic points on plane algebraic curves

  • Paul Aleksander Maugesten
  • Torgunn Karoline Moe


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.


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How to Cite
Maugesten, P., & Moe, T. (2019). The $2$-Hessian and sextactic points on plane algebraic curves. MATHEMATICA SCANDINAVICA, 125(1), 13-38.