Iterated and mixed discriminants

A. DICKENSTEIN, S. DI ROCCO, R. MORRISON

Journal of Combinatorial Algebra

European Mathematical Society

Lugar: Berlín; Año: 2023 vol. 7 p. 45 - 81

2415-6302

We consider systems of Laurent polynomials with support on a fixed pointconfiguration. In the non-defective case, the closure of the locus ofcoefficients giving a non-degenerate multiple root of the system is defined bya polynomial called the mixed discriminant. We define a related polynomialcalled the multivariate iterated discriminant, generalizing the classicalSchäfli method for hyperdeterminants. This iterated discriminant is easier tocompute and we prove that it is always divisible by the mixed discriminant. Weshow that tangent intersections can be computed via iteration if and only ifthe singular locus of a corresponding dual variety has sufficiently highcodimension. We also study when point configurations corresponding toSegre-Veronese varieties and to the lattice points of planar smooth polygons,have their iterated discriminant equal to their mixed discriminant.