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 $X^*$. We study the singular locus of projectively dual varieties of certain Segre and Plucker embeddings Complete classification of the irreducible components of the singular locus of  hyperdeterminants (i.e. Segre) is given by Weyman-Zelevinsky 96. Basically, it admits 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. We have analogous results for dual Grassmannian (i.e. Plucker) varieties.