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 skew-symmetric forms identified several defective systems. Of particular interest is when a certain secant variety Segre-Grassmann expected to fill natural ambient space, but actually hypersurface. Algorithms implemented in Bertini [6] are used determine degrees these hypersurfaces, representation-theoretic descriptions their equations given. We answer ([3], Problem 6.5), confirm speculation that each member an infinite family hypersurfaces minimally defined by (known) determinantal equation. While led numerical evidence, we provide non-numerical proofs all our results.
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