Commuting polarities and maximal partial ovoids of H(4,q2)

Abstract

AbstractIn PG(4,q2), q odd, let Q(4,q2) be a non‐singular quadric commuting with a non‐singular Hermitian variety H(4,q2). Then these varieties intersect in the set of points covered by the extended generators of a non‐singular quadric Q0 in a Baer subgeometry Σ0 of PG(4,q2). It is proved that any maximal partial ovoid of H(4,q2) intersecting Q0 in an ovoid has size at least 2(q2+1). Further, given an ovoid O of Q0, we construct maximal partial ovoids of H(4,q2) of size q3+1 whose set of points lies on the hyperbolic lines 〈P,X〉 where P is a fixed point of O and X varies in O\{P}. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 307–313, 2009