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Type: Journal article
Title: Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG(3, q)
Author: Barwick, S.
Brown, M.
Penttila, T.
Citation: Journal of Combinatorial Theory: Series A, 2006; 113(2):273-290
Publisher: Academic Press Inc Elsevier Science
Issue Date: 2006
ISSN: 0097-3165
Statement of
S.G. Barwick, Matthew R. Brown and Tim Penttila
Abstract: A flock of a quadratic cone of PG(3,q) is a partition of the non-vertex points into plane sections. It was shown by Thas in 1987 that to such flocks correspond generalized quadrangles of order (q2,q), previously constructed algebraically by Kantor (q odd) and Payne (q even). In 1999, Thas gave a geometrical construction of the generalized quadrangle from the flock via a particular set of elliptic quadrics in PG(3,q). In this paper we characterise these sets of elliptic quadrics by a simple property, construct the generalized quadrangle synthetically from the properties of the set and strengthen the main theorem of Thas 1999.
Keywords: Flock
Generalized quadrangle
Elliptic quadric
DOI: 10.1016/j.jcta.2005.03.004
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Pure Mathematics publications

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