Computations and equations for Segre-Grassmann hypersurfaces

• DOI: 10.4171/pm/1977
• Publication Date: 2016-02-25T22:45:04Z
• Authors: Noah S. Daleo; Jonathan D. Hauen...; Luke Oeding
• Keywords: Mathematics - Algebraic Geometry; FOS: Mathematics; 0101 mathematics; Algebraic Geometry (math.AG); 01 natural sciences

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.