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Geometries arising from trilinear forms on low-dimensional vector spaces

  • Ilaria Cardinali EMAIL logo and Luca Giuzzi
From the journal Advances in Geometry


Let 𝓖k(V) be the k-Grassmannian of a vector space V with dim V = n. Given a hyperplane H of 𝓖k(V), we define in [3] a point-line subgeometry of PG(V) called the geometry of poles ofH. 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 n ≤ 7 and propose some new constructions. We also extend a result of [6] regarding the existence of line spreads of PG(5, 𝕂) arising from hyperplanes of 𝓖3(V).

MSC 2010: 15A75; 14M15; 15A69
  1. Communicated by: A. Pasini


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Received: 2017-03-21
Revised: 2017-08-17
Published Online: 2019-04-09
Published in Print: 2019-04-24

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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