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arXiv · 1408.2105

Computations and Equations for Segre-Grassmann hypersurfaces

Noah S. Daleo·Jonathan D. Hauenstein·Luke Oeding
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Abstract

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.

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Noah S. Daleo, Jonathan D. Hauenstein, Luke Oeding. 2015-08-18. Computations and Equations for Segre-Grassmann hypersurfaces. https://doi.org/10.4171/pm%2F1977

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