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The generating rank of a polar Grassmannian

Ilaria Cardinali, Luca Giuzzi and Antonio Pasini
From the journal Advances in Geometry

Abstract

In this paper we compute the generating rank of k-polar Grassmannians defined over commutative division rings. Among the new results, we compute the generating rank of k-Grassmannians arising from Hermitian forms of Witt index n defined over vector spaces of dimension N > 2n. We also study generating sets for the 2-Grassmannians arising from quadratic forms of Witt index n defined over V(N, 𝔽q) for q = 4, 8, 9 and 2n ≀ N ≀ 2n + 2. We prove that for N > 6 and anisotropic defect (polar corank) d β‰  2 they can be generated over the prime subfield, thus determining their generating rank.

MSC 2010: 51A50

  1. Communicated by: H. Van Maldeghem

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Received: 2019-06-25
Revised: 2020-05-27
Published Online: 2021-07-08
Published in Print: 2021-10-26

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