Computations and equations for Segre-Grassmann hypersurfaces

Mathematics - Algebraic Geometry FOS: Mathematics 0101 mathematics Algebraic Geometry (math.AG) 01 natural sciences
DOI: 10.4171/pm/1977 Publication Date: 2016-02-25T22:45:04Z
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 [6] are used to determine the degrees of several of these hypersurfaces, and representation-theoretic descriptions of their equations are given. We answer ([3], 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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