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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), 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.
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Noah S. Daleo, Jonathan D. Hauenstein, Luke Oeding, Computations and equations for Segre-Grassmann hypersurfaces. Port. Math. 73 (2016), no. 1, pp. 71–90DOI 10.4171/PM/1977