On the irreducibility of Hessian loci of cubic hypersurfaces

Davide Bricalli, Filippo F. Favale, Gian Pietro Pirola

We study the problem of the irreducibility of the Hessian variety ${\mathcal{H}}_f$ associated with a smooth cubic hypersurface $V(f)\subset {\mathbb{P}}^n$. We prove that when $n\leq5…