A characterisation of the lines external to a quadric cone of PG\((3,q)\), \(q\) odd
type: Item
instance of: scholarly article
title: A characterisation of the lines external to a quadric cone of PG\((3,q)\), \(q\) odd
zbMATH Open document ID: 1201.51009
author: S. G. Barwick
author: David K. Butler
published in: Innovations in Incidence Geometry
publication date: 2010-09-20T00:00:00Z
review text: The authors characterise the lines not meeting a quadric cone in \(PG(3,q)\), \(q\) odd. Specifically, they prove the following. Let \({\mathcal L}\) be a non-empty set of lines in \(PG(3,q)\), \(q\) odd, such that: (1) Every point lies on \(0\), \({{1}\over{2}}q(q+1)\) or \({{1}\over{2}}q (q-1)\) lines of \({ \mathcal L}\); (2) Every plane contains \(0\), \(q^2\) or \({{1}\over{2}}q (q-1)\) lines of \({\mathcal L}\); (3) For any point \(P\), if \(P\) is on two planes which contain the same number of lines of \({\mathcal L}\), then \(P\) is on the same number of lines of \({\mathcal L}\) in both planes. Then \({\mathcal L}\) is the set of external lines to a quadric cone.
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 5788608
zbMATH Keywords: projective space
zbMATH Keywords: quadric cone
zbMATH Keywords: lines
zbMATH Keywords: characterisation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5788608