Computations and Equations for Segre-Grassmann hypersurfaces
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.
Cite
@article{arxiv.1408.2105,
title = {Computations and Equations for Segre-Grassmann hypersurfaces},
author = {Noah S. Daleo and Jonathan D. Hauenstein and Luke Oeding},
journal= {arXiv preprint arXiv:1408.2105},
year = {2025}
}
Comments
14 pages, revised content. Accepted, Portugaliae Mathematica, 2015. Updated references