Direct Constructions of Hyperplanes of Dual Polar Spaces Arising from Embeddings
โ Scribed by Bart De Bruyn
- Publisher
- Springer
- Year
- 2010
- Tongue
- English
- Weight
- 298 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0218-0006
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๐ SIMILAR VOLUMES
Let n (q) denote the geometry of the hyperbolic lines of the symplectic polar space W (2n -1, q), n 2. We show that every hyperplane of n (q) gives rise to a hyperplane of the Hermitian dual polar space DH (2n -1, q 2 ). In this way we obtain two new classes of hyperplanes of DH (2n -1, 4) which do
Let n 2, let K, K be fields such that K is a quadratic Galoisextension of K and let ฮธ denote the unique nontrivial element in Gal(K /K). Suppose the symplectic dual polar space DW (2n -1, K) is fully and isometrically embedded into the Hermitian dual polar space DH(2n -1, K , ฮธ). We prove that the p
Let 2 be a finite thick dual polar space of rank 3. We say that a hyperplane H of 2 is locally singular (respectively, quadrangular or ovoidal) if H & Q is the perp of a point (resp. a subquadrangle or an ovoid) of Q for every quad Q of 2. If H is locally singular, quadrangular, or ovoidal, then we
Let be a finite thick dual polar space, and let H be a hyperplane of . Calling the elements of of type 2 quads, we call a quad ฮฑ โ H singular (respectively subquadrangular or ovoidal) if H meets ฮฑ in the perp of a point (respectively in a full subquadrangle or in an ovoid). A hyperplane is said to b