Abstract:A hyperplane of the symplectic dual polar space DW (2n−1, F), n ≥ 2, is said to be of subspace-type if it consists of all maximal singular subspaces of W (2n − 1, F) meeting a given (n − 1)-dimensional subspace of PG(2n − 1, F). We show that a hyperplane of DW (2n − 1, F) is of subspace-type if and only if every hex F of DW (2n − 1, F) intersects it in either F , a singular hyperplane of F or the extension of a full subgrid of a quad. In the case F is a perfect field of characteristic 2, a stronger result can … Show more
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