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

摘要

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 n H is a classical ovoid of Q. (c) 2006 Elsevier Inc. All rights reserved.