On the nucleus of the Grassmmann embedding of the symplectic dual polar spaces DSp(2n,F), char(F)=2

Let n >= 3 and let F be a field of characteristic 2. Let DSp(2n, F) denote the dual polar space associated with the building of type C-n over F and let g(n-2) denote the (n - 2)-Grassmannian of type C-n. Using the bijective correspondence between the points of g(n-2) and the quads of DSp(2n, F), we construct a full projective embedding Of g(n-2) into the nucleus of the Grassmann embedding of DSp(2n. F). This generalizes a result of an earlier paper [1. Cardinali, G. Lunardon, A geometric description of the spin-embedding of symplectic dual polar spaces of rank 3, J. Combin. Theory Ser. A (in press)] which contains an alternative proof of this fact in the case when n = 3 and F is finite. (C) 2008 Elsevier Ltd. All rights reserved.