In general, two quadric surfaces intersect in a nonsingular quartic space curve. If we relax the generality assumption the intersection curve may degenerate to a finite number of different possible types of singular curves. L. Schläfli in a classical paper (1953) introduced conditions for a degenerate intersection of two surfaces of tensor type (or more generally two hypersurfaces described by multilinear equations).

In recent ongoing work with A. Dickenstein and R. Morrison we introduce a general framework which we call the iterated discriminant in order to characterize the singular intersection of hypersurfaces with a given monomial support. I will explain the basic ideas and results, especially concerning the relation between the mixed and iterated discriminant.