DW(6,n), n>2, has no ovoid: A single proof

Abstract

An ovoid of a dual polar space is a point set meeting every line in exactly one point. For the symplectic dual polar space DW(6,q), Cooperstein and Pasini have recently proved no ovoid exists if q is odd. Earlier, Shult has proved the same for even q. In this paper, we prove the non-existence of ovoids of DW(6,q) independently from the parity of q.