Iterated sparse discriminants and singular intersections of hypersurfaces

A. DICKENSTEIN

Conferencia; Boston's Joint Mathematics Colloquium (Brandeis, Harvard, MIT, and Northeastern); 2020

Northeastern University

Abstract: Itis well known that two generic quadric surfaces intersect in anonsingular quartic space curve, but when the intersection is nottransverse this intersection curve may degenerate to a finite numberof different possible types of singular curves.  In the nicepaper by Farouki et al. (1989), the authors formulate a way ofcomputing the condition for a degenerate intersection in this case,which refines in the real case and with an algorithmic point of viewa classical treatise by  Bromwich (1906). Independently,Schläfli (1953) studied the degenerate intersection of twohypersurfaces described by multilinear equations.In joint work with S. di Roccoand R. Morrison,  we present a general framework of iteratedsparse discriminants to characterize the singular intersection ofhypersurfaces with a given monomial support A, which generalizes bothprevious situations. We  study the connection of iterateddiscriminants with the notion of mixed discriminant and thesingularities of the sparse discriminant associated to A.