Iterated sparse discriminants and singular intersections of hypersurfaces

ALICIA DICKENSTEIN

Conferencia; Cattedra Fubini; 2019

It is well known that twogeneric quadric surfaces intersect in a nonsingular quartic space curve, butwhen the intersection is not transverse this intersection curve may degenerateto a finite number of different possible types of singular curves.  In thenice paper by Farouki et al. (1989), the authors formulate a way of computingthe condition for a degenerate intersection in this case, which refines in thereal case and with an algorithmic point of view a classical treatise by Bromwich (1906). Independently, Schläfli (1953) studied the degenerateintersection of two hypersurfaces described by multilinear equations.In joint work in progresswith S. di Rocco and R. Morrison,  we present a general framework ofiterated sparse discriminants to characterize the singular intersection ofhypersurfaces with a given monomial support A, which generalizes both previoussituations. We  study the connection of iterated discriminants with thenotion of mixed discriminant and the singularities of the sparse discriminantassociated to A.