On a class of hyperplanes of the symplectic and Hermitian dual polar spaces
type: Item
instance of: scholarly article
title: On a class of hyperplanes of the symplectic and Hermitian dual polar spaces
zbMATH Open document ID: 1169.51003
published in: The Electronic Journal of Combinatorics
publication date: 2009-04-07T00:00:00Z
full work available at URL: https://eudml.org/doc/130485
full work available at URL: v16i1r1.html
review text: The author defines a class of hyperplanes of a symplectic dual polar space \(DW(2n-1,{\mathbb K})\) or a Hermitian dual polar space \(DH(2n-1,{\mathbb K},\theta), n \geq 2\) and discuss several properties of these hyperplanes. He shows that there exists an ovoid of the Hermitian dual polar space \(DH(2n-1,{\mathbb K},\theta)\) arising from its Grassmann-embedding if and only if there exists an empty theta-Hermitian variety in \({\text PG}(n-1,{\mathbb K})\) and he gives the first examples of ovoids in thick dual polar spaces of rank at least 3 which arise from some projective embedding.
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 51A50
zbMATH DE Number: 5541066
zbMATH Keywords: symplectic dual polar space
zbMATH Keywords: Hermitian dual polar space
zbMATH Keywords: hyperplane
zbMATH Keywords: Grassmann-embedding
zbMATH Keywords: ovoid
author: Bart De Bruyn
reviewed by: Süleyman Çiftçi
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5541066