On a class of hyperplanes of the symplectic and Hermitian dual polar spaces
The author defines a class of hyperplanes of a symplectic dual polar space \(DW(2n-1,{\mathbb K})\) or a Hermitian dual polar space \(DH(2n-1,{\mathbb K},\theta), n \geq 2\) and discuss several properties of these hyperplanes. He shows that there exists an ovoid of the Hermitian dual polar space \(DH(2n-1,{\mathbb K},\theta)\) arising from its Grassmann-embedding if and only if there exists an empty theta-Hermitian variety in \({\text PG}(n-1,{\mathbb K})\) and he gives the first examples of ovoids in thick dual polar spaces of rank at least 3 which arise from some projective embedding.
scientific article; zbMATH DE number 5541066