Hyperbolic fibrations of \(\text{PG}(3,q)\)
type: Item
instance of: scholarly article
title: Hyperbolic fibrations of \(\text{PG}(3,q)\)
zbMATH Open document ID: 0923.51005
author: R. D. Baker
author: Jeremy M. Dover
author: Gary L. Ebert
author: K. L. Wantz
published in: European Journal of Combinatorics
publication date: 1999-04-11T00:00:00Z
review text: A hyperbolic fibration of \(\text{PG}(3,q)\) is a set of \(q-1\) hyperbolic quadrics in \(\text{PG}(3,q)\) and two lines that together partition the point set of \(\text{PG}(3,q)\). For \(q\) odd, the authors review the known fibrations and construct a new family from a pencil of quadrics (containing a line as a reducible quadric) by replacing the set of \({1\over 2}(q+1)\) elliptic quadrics of the pencil by \({1\over 2}(q-1)\) hyperbolic quadrics and a line. Spreads can be obtained from a fibration by taking the two special lines, and by taking a regulus in each hyperbolic quadric. This way, the authors obtain new spreads from their new fibrations. They investigate the automorphism group of such spreads, and they conjecture that for \(q\geq 9\) these spreads contain only the \(q-1\) reguli of the hyperbolic quadrics of the fibration.
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 1251345
zbMATH Keywords: translation plane
zbMATH Keywords: hyperbolic fibration
zbMATH Keywords: regulus
zbMATH Keywords: spreads
reviewed by: Hendrik Van Maldeghem
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: eujc.1998.0249
OpenAlex ID: W2065619330
DOI: 10.1006/EUJC.1998.0249
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description: scientific article; zbMATH DE number 1251345