Geometry Seminar
Date: October 13, 2017
Time: 4:00PM - 5:00PM
Location: BLOC 628
Speaker: Emre Sen, Northeastern
Title: Singularities of dual varieties associated to exterior representations
Abstract: For a given irreducible projective variety $X$, the closure of the set of all hyperplanes containing tangents to $X$ is the projectively dual variety $X^{\vee}$. We study the singular locus of projectively dual varieties of certain Segre-Pl\"{u}cker embeddings. We give a complete classification of the irreducible components of the singular locus of several representation classes. Basically, they admit two types of singularities: cusp type and node type which are degeneracies of a certain Hessian matrix, and the closure of the set of tangent planes having more than one critical point respectively. In particular, our results include a description of singularities of dual Grassmannian varieties.