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 ≠ 2 they can be generated over the prime subfield, thus determining their generating rank.

Cardinali, I., Giuzzi, L., Pasini, A. (2021). The generating rank of a polar Grassmannian. ADVANCES IN GEOMETRY, 21(4), 515-539 [10.1515/advgeom-2021-0022].

The generating rank of a polar Grassmannian

Cardinali I.
;
2021

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 ≠ 2 they can be generated over the prime subfield, thus determining their generating rank.
Cardinali, I., Giuzzi, L., Pasini, A. (2021). The generating rank of a polar Grassmannian. ADVANCES IN GEOMETRY, 21(4), 515-539 [10.1515/advgeom-2021-0022].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1179114