Collineations and dualities of partial geometries

In this paper, we first prove some general results on the number of fixed points of collineations of finite partial geometries, and on the number of absolute points of dualities of partial geometries. In the second part of the paper, we establish the number of isomorphism classes of partial geometries arising from a Thas maximal arc constructed from a (finite) Suzuki-Tits ovoid in a classical projective plane. We also determine the full automorphism group of these structures, and show that every partial geometry arising from any Thas maximal arc is self-dual.

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Beukje Temmermans, Joseph A. Thas, Hendrik Van Maldeghem
• Keywords: Classical Projective Plane, DM 2010, Partial Geometries, Thas Maximal Arc