Ovoids, Spreads and Self-Dual Polygons

Abstract

Ovoids and spreads are in more than one respect special configurations in generalized polygons. Roughly speaking, an ovoid in a generalized polygon is a set of mutually opposite points “of maximal size” (this will be made precise below for infinite polygons), and the dual notion is a spread. Sets of maxial size with respect to a certain property in geometries usually themselves have interesting properties. For example, they might be used to construct other geometries (as ovoids in projective spaces are used to construct generalized quadrangles