  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.
