On the hyperplanes of the half-spin geometries and the dual polar spaces DQ(2n,K)

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 3
Cited 2

Valuations and hyperplanes of dual polar spaces

Journal of Combinatorial Theory Series A
Locally singular hyperplanes in thick dual polar spaces of rank 4

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

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Note: Two classes of hyperplanes of dual polar spaces without subquadrangular quads

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On geometric SDPS-sets of elliptic dual polar spaces

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Abstract

We describe relationships between locally singular hyperplanes of the dual polar space DQ(2n,K), n=2, and hyperplanes of the half-spin geometries HS(2n-1,K) and HS(2n+1,K) for the respective hyperbolic quadrics Q^+(2n-1,K) and Q^+(2n+1,K). We use these relationships to classify all hyperplanes of HS(9,K) and to provide a method for constructing locally singular hyperplanes of DQ(2n+2,K) from locally singular hyperplanes of DQ(2n,K). Along our way, we also obtain a new proof for the fact that all hyperplanes of the half-spin geometries arise from embeddings.