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Geometries arising from trilinear forms on low-dimensional vector spaces | | Ilaria Cardinali
; Luca Giuzzi
; | | Date: |
20 Mar 2017 | | Abstract: | Let ${mathcal G}_k(V)$ be the $k$-Grassmannian of a vector space $V$ with
$dim V=n$. Given a hyperplane $H$ of ${mathcal G}_k(V)$, we define in [I.
Cardinali, L. Giuzzi, A. Pasini, A geometric approach to alternating $k$-linear
forms, J. Algebraic Combin. doi:10.1007/s10801-016-0730-6] a point-line
subgeometry of ${mathrm{PG}}(V)$ called the {it geometry of poles of $H$}. In
the present paper, exploiting the classification of alternating trilinear forms
in low dimension, we characterize the possible geometries of poles arising for
$k=3$ and $nleq 7$ and propose some new constructions. We also extend a result
of [J.Draisma, R. Shaw, Singular lines of trilinear forms, Linear Algebra Appl.
doi:10.1016/j.laa.2010.03.040] regarding the existence of line spreads of
${mathrm{PG}}(5,{mathbb K})$ arising from hyperplanes of ${mathcal G}_3(V).$ | | Source: | arXiv, 1703.6821 | | Services: | Forum | Review | PDF | Favorites | |
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