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arXiv · 1709.01698

The 2-Hessian and sextactic points on plane algebraic curves

Paul Aleksander Maugesten·Torgunn Karoline Moe
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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.

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Paul Aleksander Maugesten, Torgunn Karoline Moe. 2017-09-06. The 2-Hessian and sextactic points on plane algebraic curves. https://doi.org/10.7146/math.scand.a-114715

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