The general ternary form can be recovered by its Hessian

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 $d\ge 4$, $d\ne 5$, by considering the action of the orthogonal group. In a previous paper we proved the analogous result for binary forms, with more geometric techniques.

by Ciro Ciliberto, Giorgio Ottaviani, with an appendix by Jerson Caro, Juanita Duque-Rosero

Cited by in corpus (1)

• On the irreducibility of Hessian loci of cubic hypersurfaces