Abstract :
In 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.
