Linear representation of Buekenhout–Metz unitals

AbstractIn the linear representation of the desarguesian plane PG(2,q2) in PG(5,q), the classical unital (the hermitian curve) is represented by an elliptic quadric ruled by lines of a normal spread. In this paper, we prove that a Buekenhout–Metz unital U in PG(2,q2), arising from an elliptic quadric, is represented in PG(5,q) by an algebraic hypersurface of degree four minus the complement of a line in a three-dimensional subspace. Also, such a hypersurface is reducible if and only if U is classical