A characterization of a class of hyperplanes of DW(2n1,F)
Pages 3176 - 3182
Abstract
A hyperplane of the symplectic dual polar space DW(2n1,F), n2, is said to be of subspace-type if it consists of all maximal singular subspaces of W(2n1,F) meeting a given (n1)-dimensional subspace of PG(2n1,F). We show that a hyperplane of DW(2n1,F) is of subspace-type if and only if every hex F of DW(2n1,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 be proved, namely a hyperplane H of DW(2n1,F) is of subspace-type or arises from the spin-embedding of DW(2n1,F)DQ(2n,F) if and only if every hex F intersects it in either F, a singular hyperplane of F, a hexagonal hyperplane of F or the extension of a full subgrid of a quad.
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Published: 06 January 2017
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