Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG(3, q)
Date
2006
Authors
Barwick, S.
Brown, M.
Penttila, T.
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Advisors
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Volume Title
Type:
Journal article
Citation
Journal of combinatorial theory. Series A, 2006; 113(2):273-290
Statement of Responsibility
S.G. Barwick, Matthew R. Brown and Tim Penttila
Conference Name
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.