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arXiv · 2406.05382

The general ternary form can be recovered by its Hessian

Ciro Ciliberto·Giorgio Ottaviani·Jerson Caro·Juanita Duque-Rosero
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Abstract

The Hessian map is the rational map that sends a homogeneous polynomial to the determinant of its Hessian matrix. We prove that the Hessian map is birational on its image for ternary forms of degree $d\ge 4$, $d\neq 5$, by considering the action of the orthogonal group. In a previous paper we proved the analogous result for binary forms, with more geometric techniques.

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Ciro Ciliberto, Giorgio Ottaviani, Jerson Caro, Juanita Duque-Rosero. 2024-06-08. The general ternary form can be recovered by its Hessian. https://arxiv.org/abs/2406.05382

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