A characterization of a class of hyperplanes of DW2n-1, FReport as inadecuate




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(2017)DISCRETE MATHEMATICS.340(1).p.3176-3182 Mark 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 IF is a perfect field of characteristic 2, a stronger result can be proved, namely a hyperplane H of DW(2n - 1, F) is of subspace-type or arises from the spin-embedding of DW(2n - 1, F) congruent to 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. (C) 2016 Elsevier B.V. All rights reserved.

Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8510624



Author: Bart De Bruyn

Source: https://biblio.ugent.be/publication/8510624



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