κ-arcs and partial flocks

Abstract

Using the relationship between partial flocks of the quadratic cone K in PG(3, q), q even, and arcs in the plane PG(2, q), new results on partial flocks and short proofs for known theorems on translation generalized quadrangles of order (q(2), q) and on ovoids in PC(3, q) are obtained. It is shown that large partial flocks of K containing approximately q conics, q even, are always extendable to a flock, which improves a result by Payne and Thas. Then new and short proofs are given for a theorem of Johnson on translation generalized quadrangles and a theorem of Glynn on ovoids