The hyperplanes of \(DW(5,2^h)\)which arise from embedding
It is shown that there are six isomorphism classes of hyperplanes of the dual polar space \(\varDelta =DW(5,2^h\)) which arise from the Grassmann-embedding. If \(h\geq 2\), then these are all the hyperplanes of \(\varDelta \) arising from an embedding. If \(h=1\), then there are 6 extra classes of hyperplanes as has been shown by \textit{H. Pralle} [Exp. Math. 14, No. 3, 373--384 (2005; Zbl 1093.51012)] with the aid of a computer. A computer-free proof for this fact is presented here. The hyperplanes of \(DW(5,q), q\) odd, arising from an embedding will be classified in the forthcoming paper [\textit{B. N. Cooperstein} and \textit{B. De Bruyn}, ``Points and hyperplanes of the universal embedding space of the dual polar space \(DW(5,q),q\) odd'', Mich. Math. J. (in press)].
scientific article; zbMATH DE number 5499899
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