The hyperplanes of DQ(2n,K) and DQ-(2n+1,q) which arise from their spin-embeddings

Authors:
Bart De Bruyn
Affiliations:
Ghent University, Department of Pure Mathematics and Computer Algebra, Galglaan 2, B-9000 Gent, Belgium
Venue:
Journal of Combinatorial Theory Series A
Year:
2007

Citing 6
Cited 6

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Abstract

We characterize the hyperplanes of the dual polar spaces DQ(2n,K) and DQ^-(2n+1,q) which arise from their respective spin-embeddings. The hyperplanes of DQ(2n,K) which arise from its spin-embedding are precisely the locally singular hyperplanes of DQ(2n,K). The hyperplanes of DQ^-(2n+1,q) which arise from its spin-embedding are precisely the hyperplanes H of DQ^-(2n+1,q) which satisfy the following property: if Q is an ovoidal quad, then Q@?H is a classical ovoid of Q.