Coordinate sections of generic Hankel matrices

Abstract

One deals with degenerations by coordinate sections of the square generic Hankel matrix over a field $k$ of characteristic zero, along with its main related structures, such as the determinant of the matrix, the ideal generated by its partial derivatives, the polar map defined by these derivatives, the Hessian matrix and the ideal of the submaximal minors of the matrix. It is proved that the polar map is dominant for any such degenerations, and not homaloidal in the generic case. The problem of whether the determinant $f$ of the matrix is a factor of the Hessian with the (Segre) expected multiplicity is considered, for which the expected lower bound of the dual variety of $V(f)$ is established.