TY - JOUR
AU - Paul Maugesten
AU - Torgunn Moe
PY - 2019/08/29
Y2 - 2020/08/09
TI - The $2$-Hessian and sextactic points on plane algebraic curves
JF - MATHEMATICA SCANDINAVICA
JA - MathScand
VL - 125
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-114715
UR - https://www.mscand.dk/article/view/114715
AB - 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.
ER -