Transitive ovoids of the Hermitian surface of PG(3,q2), q even

A. Cossidente, G. Korchmáros
2003 Journal of combinatorial theory. Series A  
As it is well known, the transitive ovoids of PGð3; qÞ are the non-degenerate quadrics and the Suzuki-Tits ovoids (see in: A. classified the 2-transitive ovoids of finite classical polar spaces. Kleidman's result was partially improved by Gunawardena (J. Combin. Theory Ser. A 89 (2000) 70) who determined the primitive ovoids of the quadric O þ 8 ðqÞ: Transitive ovoids of the classical polar space arising from the Hermitian surface Hð3; q 2 Þ of PGð3; q 2 Þ with even q are investigated in this
more » ... per. There are known two such ovoids up to projectivity, namely the classical ovoid and the Singertype ovoid. Both are linearly transitive in the sense that the subgroup of PGUð4; q 2 Þ preserving the ovoid is still transitive on it. Furthermore, the full collineation group preserving either of them is a subgroup of PGUð3; q 2 Þ: Our main result states that for q even the only linearly transitive ovoids are the classical ovoids and the Singer-type ovoid. It remains open the problem of finding other (i.e. non-linearly) transitive ovoids, although we prove that the full collineation group of any transitive ovoid is a subgroup of PGUð3; q 2 Þ: r
doi:10.1016/s0097-3165(02)00021-3 fatcat:shihiwhma5hkxh4hhvcb7anxcm