Iterated and mixed discriminants

Classical work by Salmon and Bromwich classified singular intersections of two quadric surfaces. The basic idea these results was already pursued Cayley in connection with tangent conics the plane used Schäfli for study hyperdeterminants. More recently, problem has been revisited similar tools context geometric modeling a generalization to case higher dimensional hypersurfaces given Ottaviani. We propose this question systems Laurent polynomials support on fixed point configuration. In non-defective case, closure locus coefficients giving non-degenerate multiple root system is defined polynomial called mixed discriminant. define related multivariate iterated discriminant, generalizing classical method This discriminant easier compute we prove that it always divisible show can be computed via iteration if only corresponding dual variety sufficiently high codimension. also when configurations Segre–Veronese varieties lattice points planar smooth polygons, have their equal