June 8, 2024Open Access

The general ternary form can be recovered by its Hessian

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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 4, d 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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Ciliberto et al. (Sat,) studied this question.

synapsesocial.com/papers/68e65993b6db6435875e87f5 https://doi.org/https://doi.org/10.48550/arxiv.2406.05382

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