Symmetry preserving degenerations of the generic symmetric matrix

Abstract

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 $V(f)$.

34 pages.This is a revised version. The introduction has been modified and we include new bibliographic references. arXiv admin note: text overlap with arXiv:1610.07681