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

✍ Scribed by Antonio Cossidente; Alessandro Siciliano

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 111 KB
• Volume: 17
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20212

✦ Synopsis

Abstract

In PG(4,q^2^), q odd, let Q(4,q^2^) be a non‐singular quadric commuting with a non‐singular Hermitian variety H(4,q^2^). Then these varieties intersect in the set of points covered by the extended generators of a non‐singular quadric Q~0~ in a Baer subgeometry Σ~0~ of PG(4,q^2^). It is proved that any maximal partial ovoid of H(4,q^2^) intersecting Q~0~ in an ovoid has size at least 2(q^2^+1). Further, given an ovoid O of Q~0~, we construct maximal partial ovoids of H(4,q^2^) of size q^3^+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