Generalising a characterisation of Hermitian curves

Abstract

This article proves a characterisation of the classical unital that is a generalisation of a characterisation proved in 1982 by Lefèvre-Percsy. It is shown that if U is a Buekenhout-Metz unital with respect to a line l∞ in PG(2, q²) such that a line of PG(2, q²) not through U Ո l∞ meets U in a Baer subline, then U is classical. An immediate corollary is that if U is a unital in PG(2, q²) such that U is Buekenhout-Metz with respect to two distinct lines, then U is classical.