TY - JOUR AU - Maugesten, Paul Aleksander AU - Moe, Torgunn Karoline PY - 2019/08/29 Y2 - 2024/03/29 TI - The $2$-Hessian and sextactic points on plane algebraic curves JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 125 IS - 1 SE - Articles DO - 10.7146/math.scand.a-114715 UR - https://www.mscand.dk/article/view/114715 SP - 13-38 AB - <p>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.</p> ER -