The general ternary form can be recovered by its Hessian
Algebraic Geometry
2025-03-13 v2
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 , , by considering the action of the orthogonal group. In a previous paper we proved the analogous result for binary forms, with more geometric techniques.
Cite
@article{arxiv.2406.05382,
title = {The general ternary form can be recovered by its Hessian},
author = {Ciro Ciliberto and Giorgio Ottaviani and Jerson Caro and Juanita Duque-Rosero},
journal= {arXiv preprint arXiv:2406.05382},
year = {2025}
}
Comments
by Ciro Ciliberto, Giorgio Ottaviani, with an appendix by Jerson Caro, Juanita Duque-Rosero