Ovoids of the quadric Q\((2n,q)\)
type: Item
instance of: scholarly article
title: Ovoids of the quadric Q\((2n,q)\)
zbMATH Open document ID: 0819.51005
DOI: 10.1016/0195-6698(95)90092-6
author: Christine M. O'Keefe
author: Joseph A. Thas
published in: European Journal of Combinatorics
publication date: 1995-08-27T00:00:00Z
review text: Let \(Q(2n,q)\) be a nonsingular quadric in the projective space \(PG (2n,q)\) for \(n \geq 2\). An avoid of \(Q(2n,q)\) is a set of points of \(Q(2n,q)\) which has exactly one point in common with each subspace of maximal dimension on \(Q(2n,q)\). The authors prove that if \(q\) is odd, \(q \neq 3\), and every ovoid of the nonsingular quadric \(Q(4,q)\) in \(PG(4,q)\) is an elliptic quadric, then \(Q(6,q)\), and hence also \(Q(2n,q)\) with \(n \geq 3\), has no ovoid. As a corollary, it follows that \(Q(2n,5)\) and \(Q(2n,7)\), \(n \geq 3\), have no ovoid. Also, a survey of the known results about existence and non-existence of ovoids in \(Q(2n,q)\) is given.
reviewed by: Anatoli Kondrat'ev
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 731898
zbMATH Keywords: finite projective space
zbMATH Keywords: quadric
zbMATH Keywords: ovoid
MaRDI profile type: Publication
full work available at URL: 0195-6698(95)90092-6
OpenAlex ID: W2082968562
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description: scientific article; zbMATH DE number 731898