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arXiv · 2407.16582

Eigenpoint collinearities of plane cubics

Valentina Beorchia·Matteo Gallet·Alessandro Logar
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Abstract

Given a ternary homogeneous polynomial, the fixed points of the map from $\mathbb{P}^2$ to itself defined by its gradient are called its eigenpoints. We focus on cubic polynomials, and analyze configurations of eigenpoints that admit one or more alignments. We give a classification and explicit equations, in the coordinates of the points, of all configurations: this is accomplished by using both geometric techniques and by an extensive use of computer algebra.

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Valentina Beorchia, Matteo Gallet, Alessandro Logar. 2024-07-23. Eigenpoint collinearities of plane cubics. https://arxiv.org/abs/2407.16582

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