  One considers certain degenerations of the generic symmetric matrix over a
field $k$ of characteristic zero and the main structures related to the
determinant $f$ of the matrix, such as the ideal generated by its partial
derivatives, the polar map defined by these derivatives and its image $V(f)$,
the Hessian matrix, the ideal and the map given by the cofactors, and the dual
variety of $V(f)$.
