BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alicia Dickenstein (Universidad de Buenos Aires) DTSTART:20220222T150000Z DTEND:20220222T160000Z DTSTAMP:20260423T053014Z UID:ZAG/187 DESCRIPTION:Title: It erated and mixed discriminants\nby Alicia Dickenstein (Universidad de Buenos Aires) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstra ct\nClassical work by Salmon and Bromwich classified singular intersection s of two quadric surfaces. The basic idea of these results was already pur sued by Cayley in connection with tangent intersections of conics in the p lane and used by Schafli for the study of hyperdeterminants. More recently \, the problem has been revisited with similar tools in the context of geo metric modeling and a generalization to the case of two higher dimensional quadric hypersurfaces was given by Ottaviani. In joint work with Sandra d i Rocco and Ralph Morrison\, we propose and study a generalization of this question for systems of Laurent polynomials with support on a fixed point configuration. In the non-defective case\, the closure of the locus of co efficients giving a non-degenerate multiple root of the system is defined by a polynomial called the mixed discriminant. We define a related polynom ial called the multivariate iterated discriminant. This iterated discrimin ant is easier to compute and we prove that it is always divisible by the m ixed discriminant. We show that tangent intersections can be computed via iteration if and only if the singular locus of a corresponding dual variet y has sufficiently high codimension. We also study when point configuratio ns corresponding to Segre-Veronese varieties and to the lattice points of planar smooth polygons\, have their iterated discriminant equal to their m ixed discriminant.\n LOCATION:https://researchseminars.org/talk/ZAG/187/ END:VEVENT END:VCALENDAR