The 2-Hessian and sextactic points on plane algebraic curves
Abstract
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.
Cite
@article{arxiv.1709.01698,
title = {The 2-Hessian and sextactic points on plane algebraic curves},
author = {Paul Aleksander Maugesten and Torgunn Karoline Moe},
journal= {arXiv preprint arXiv:1709.01698},
year = {2019}
}
Comments
Updated version to be published in Mathematica Scandinavica. Substantially rewritten, but with essential results unchanged. Contains results from first author's master's thesis. 21 pages, 2 figures