INVESTIGADORES
DICKENSTEIN Alicia Marcela
artículos
Título:
Iterated and mixed discriminants
Autor/es:
A. DICKENSTEIN, S. DI ROCCO, R. MORRISON
Revista:
Journal of Combinatorial Algebra
Editorial:
European Mathematical Society
Referencias:
Lugar: Berlín; Año: 2023 vol. 7 p. 45 - 81
ISSN:
2415-6302
Resumen:
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.