The general ternary form can be recovered by its Hessian (with an appendix by Jerson Caro and Juanita Duque-Rosero)
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.
Fields of Study & Subjects
Geometry and complex manifolds
Polynomial and algebraic computation
Quantum chaos and dynamical systems
Publication details
- Journal / source
- Documenta Mathematica
- Publisher
- European Mathematical Society - EMS - Publishing House GmbH
- Volume
- 31
- Issue
- 4
- Pages
- 983–1010
- Publication date
- 13 May 2026
- Language
- EN