The generating rank of a polar Grassmannian-Reference-Cited by-同舟云学术

The generating rank of a polar Grassmannian

Published:2021-07-08 Issue:4 Volume:21 Page:515-539
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Cardinali Ilaria¹,Giuzzi Luca²,Pasini Antonio¹

Affiliation:

1. Department of Information Engineering and Mathematics , University of Siena , Via Roma 56, 53100 , Siena , Italy

2. D.I.C.A.T.A.M, Section of Mathematics, Università di Brescia , Via Branze 53, 25123 , Brescia , Italy

Abstract

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, 𝔽 q ) 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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2021-0022/pdf

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