Tubes in PG(3, q)

Peter Cameron*, Norbert Knarr

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

A tube (resp. an oval tube) in PG(3, q) is a pair T = {L, L}, where {L} ∪ L is a collection of mutually disjoint lines of PG(3, q) such that for each plane π of PG(3, q) containing L, the intersection of π with the lines of L is a hyperoval (resp. an oval). The line L is called the axis of T. We show that every tube for q even and every oval tube for q odd can be naturally embedded into a regular spread and hence admits a group of automorphisms which fixes every element of T and acts regularly on each of them. For q odd we obtain a classification of oval tubes up to projective equivalence. Furthermore, we characterize the reguli in PG(3, q), q odd, as oval tubes which admit more than one axis.

Original languageEnglish
Pages (from-to)114-124
Number of pages11
JournalEuropean Journal of Combinatorics
Volume27
Issue number1
DOIs
Publication statusPublished - 1 Jan 2006

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