Degenerating discriminants

For a flat family of projective varieties, it is natural to ask what is the behavior of dual and conormal varieties of the fibers. We study the limit of the latter using theory of Whitney stratifications. For special families we describe the limit explicitly both set- and scheme-theoretically. In some cases, this allows us to understand the degree of the dual variety of the general fiber. We then apply this theory to the study of discriminants for parametrized systems and multigrades higher associated hypersurfaces in the product of Grassmannians. The latter uses generalized Cayley trick. Based on joint work with Viktoriia Borovik.