Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG\((3,q)\)
type: Item
instance of: scholarly article
title: Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG\((3,q)\)
zbMATH Open document ID: 1088.51001
author: Matthew Brown
author: Tim Penttila
author: S. G. Barwick
published in: Journal of Combinatorial Theory. Series A
publication date: 2006-03-16T00:00:00Z
review text: \textit{J. A. Thas} showed in [Eur. J. Comb. 8, 441--452 (1987; Zbl 0646.51019)] that every flock of a quadratic cone of PG\((3,q\)) gives rise to a generalized quadrangle of order \((q,q^2)\). In 1999, \textit{J. A. Thas} [J. Comb. Theory, Ser. A 87, No. 2, 247--272 (1999; Zbl 0949.51003)] provided a geometrical construction of such generalized quadrangles by using a particular set of elliptic quadrics (called a tetradic set) in PG\((3,q \)). The authors of the manuscript under review characterize such tetradic sets and construct the associated generalized quadrangle synthetically from out of this characterization. As a result, this strengthens J. A. Thas' main theorem in [1999 (loc. cit.)].
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E12
zbMATH DE Number: 5012960
zbMATH Keywords: flock
zbMATH Keywords: generalized quadrangle
zbMATH Keywords: elliptic quadric
MaRDI profile type: Publication
full work available at URL: j.jcta.2005.03.004
OpenAlex ID: W2049314439
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DOI: 10.1016/J.JCTA.2005.03.004
description: scientific article; zbMATH DE number 5012960