%0 Journal Article
%T Computations and Equations for Segre-Grassmann hypersurfaces
%A Noah S. Daleo
%A Jonathan D. Hauenstein
%A Luke Oeding
%J Mathematics
%D 2014
%I arXiv
%X In 2013, Abo and Wan studied the analogue of Waring's problem for systems of skew-symmetric forms and identified several defective systems. Of particular interest is when a certain secant variety of a Segre-Grassmann variety is expected to fill the natural ambient space, but is actually a hypersurface. Algorithms implemented in Bertini are used to determine the degrees of several of these hypersurfaces, and representation-theoretic descriptions of their equations are given. We answer Problem 6.5 [Abo-Wan2013], and confirm their speculation that each member of an infinite family of hypersurfaces is minimally defined by a (known) determinantal equation. While led by numerical evidence, we provide non-numerical proofs for all of our results.
%U http://arxiv.org/abs/1408.2105v3