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GASC Seminar "Iterated discriminants and singular space curves" by Alicia Dickenstein (University of Buenos Aires)

Abstract: In general, two quadric surfaces intersect in a nonsingular quartic space curve. If we relax the generic assumption, the intersection curve may degenerate to a finite number of different possible types of singular curves. The classification of such singular intersections goes back to T. J. I'A. Bromwich (1906). This was studied with an emphasis on the real case in the context of geometric modeling by R. T. Farouki et al. (1989). On the other side, L. Schläfli (1953) introduced conditions for a degenerate intersection of two surfaces of tensor type (or more generally, hypersurfaces described by multilinear equations).

Folllowing ongoing joint work with S. di Rocco and R. Morrison, I will present a general framework of iterated discriminants to characterize the singular intersection of hypersurfaces with a given monomial support, which generalizes both previous situations.  I will explain the notion of mixed discriminant and the relation with these iterated discriminants. 

(Note unusual seminar time.)

Monday, October 29, 2018 at 3:00pm to 4:00pm

511 Lake Hall

Event Type

Seminar

Departments

COS, Mathematics, Geometry, Algebra, Singularities, Combinatorics (GASC)

Sponsoring Organization

Mathematics Department

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