The non-existence of ovoids in \(O_ \nu (q)\)
type: Item
instance of: scholarly article
title: The non-existence of ovoids in \(O_ \nu (q)\)
zbMATH Open document ID: 0872.51005
author: Athula Gunawardena
author: G. Eric Moorhouse
published in: European Journal of Combinatorics
publication date: 1997-10-15T00:00:00Z
review text: The authors show that the parabolic quadric \(Q (2n,q)\), \(q\) odd, in the projective space \(PG (2n,q)\) does not admit avoids whenever \(n\geq 4\). Their method runs as follows: they associate a certain two-graph to an ovoid and then they show that this two-graph is regular. They calculate the eigenvalues and multiplicities of the corresponding \((0, \pm 1)\)-adjacency matrix. The result follows from expressing that these multiplicities are integers.
Mathematics Subject Classification ID: 51A50
zbMATH DE Number: 986979
zbMATH Keywords: parabolic quadric
zbMATH Keywords: avoids
zbMATH Keywords: two-graph
reviewed by: Hendrik Van Maldeghem
MaRDI profile type: Publication
full work available at URL: eujc.1996.0084
OpenAlex ID: W2098969247
DOI: 10.1006/EUJC.1996.0084
description: scientific article; zbMATH DE number 986979