Iterated sparse discriminants and singular intersections of hypersurfaces

A, DICKENSTEIN

Congreso; Seminario Cruz del Sur; 2020

Universidad de la Frontera

It is well known that two generic quadric surfaces intersect in a nonsingular quartic space curve, but when the intersection is not transverse this intersection curve may degenerate to a finite number of different possible types of singular curves.  In the nice paper by Farouki et al. (1989), the authors formulate a way of computing the condition for a degenerate intersection in this case, which refines in the real case and with an algorithmic point of view a classical treatise by  Bromwich (1906). Independently,Schläfli (1953) studied the degenerate intersection of two hypersurfaces described by multilinear equations.In joint work with S. di Rocco and R. Morrison,  we present a general framework of iterated sparse discriminants to characterize the singular intersection of hypersurfaces with a given monomial support A, which generalizes bothprevious situations. We  study the connection of iterated discriminants with the notion of mixed discriminant and the singularities of the sparse discriminant associated to A.