Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG(3,q)

S.G. Barwick, Matthew R. Brown, Tim Penttila
2006 Journal of combinatorial theory. Series A  
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 (q 2 , 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
more » ... property, construct the generalized quadrangle synthetically from the properties of the set and strengthen the main theorem of Thas 1999.
doi:10.1016/j.jcta.2005.03.004 fatcat:jprgevs7z5e2hf7zoalrl5c5o4