3 problems

Let $f$ define a hypersurface whose Hessian determinant vanishes identically. A hypersurface is a cone if it is projectively a cone over a lower-dimensional projective variety. Hes…

Let $H_f$ be the Hessian matrix of the determinant $f=\det(P_T)$ of the Padé matrix in the cases covered by the vanishing-Hessian discussion, and let the generic corank mean the di…

Let $\mathsc{A}$ be the Coxeter arrangement associated with a finite reflection group $W$. The Hessian rank conjecture. The Hessian rank condition holds for $\mathsc{A}$ if $W$ is…