TY - JOUR
T1 - Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG(3, q)
AU - Barwick, S.G.
AU - Brown, M.R.
AU - Penttila, Tim
PY - 2006
Y1 - 2006
N2 - 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 property, construct the generalized quadrangle synthetically from the properties of the set and strengthen the main theorem of Thas 1999. (c) 2005 Elsevier Inc. All rights reserved.
AB - 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 property, construct the generalized quadrangle synthetically from the properties of the set and strengthen the main theorem of Thas 1999. (c) 2005 Elsevier Inc. All rights reserved.
U2 - 10.1016/j.jcta.2005.03.004
DO - 10.1016/j.jcta.2005.03.004
M3 - Article
SN - 0097-3165
VL - 113
SP - 273
EP - 290
JO - Journal of Combinatorial Theory Series A
JF - Journal of Combinatorial Theory Series A
IS - 2
ER -