On the nucleus of the Grassmann embedding of the symplectic dual polar space $DSp(2n,F)$.

Let \geq 3$ and let $ be a field of characteristic 2. Let (2n,F)$ denote the dual polar space associated with the building of Type $ over $ and let $\mathcal{G}_{n-2}$ denote the $(n-2) of type $. Using the bijective correspondence between the points of $\mathcal{G}_{n-2}$ and the quads of (2n,F)$,we construct a full projective embedding of $\mathcal{G}_{n-2}$ into the nucleus of the Grassmann embedding of (2n,F)$. This generalizes a result of Cardinali and Lunardon which contains an alternative proof ofthis fact in the case when =3$ and $ is finite.Let \geq 3$ and let $ be a field of characteristic 2. Let (2n,F)$ denote the dual polar space associated with the building of Type $ over $ and let $\mathcal{G}_{n-2}$ denote the $(n-2) of type $. Using the bijective correspondence between the points of $\mathcal{G}_{n-2}$ and the quads of (2n,F)$,we construct a full projective embedding of $\mathcal{G}_{n-2}$ into the nucleus of the Grassmann embedding of (2n,F)$. This generalizes a result of Cardinali and Lunardon which contains an alternative proof ofthis fact in the case when =3$ and $ is finite.A