Feet in orthogonal-Buekenhout–Metz unitals

Abstract

Given an Orthogonal-Buekenhout-Metz unital U α,β , embedded in P G(2, q 2 ), and a point P / ∈ U α,β , we study the set of feet, τ P (U α,β ), of P in U α,β . We characterize geometrically each of these sets as either q + 1 collinear points or as q + 1 points partitioned into two arcs. Other results about the geometry of these sets are also given.