A combinatorial characterization of classical unitals

Abstract.

In this paper we give a characterization of classical unitals in terms of a configuration pattern formed by the feet of a unital U embedded in PG(2, q ²), q > 2. We show that a necessary and sufficient condition for U to be classical is the existence of two points $p_0, p_1 \in U$ with tangent lines L ₀ and L ₁, respectively, such that for all points $r \in L_0 \backslash \{p_0\}$ and $s \in L_1 \backslash \{p_1\}$ the corresponding feet are collinear.