The hyperplanes of finite symplectic dual polar spaces which arise from projective embeddings
نویسندگان
چکیده
منابع مشابه
Locally subquadrangular hyperplanes in symplectic and Hermitian dual polar spaces
In [11] all locally subquadrangular hyperplanes of finite symplectic and Hermitian dual polar spaces were determined with the aid of counting arguments and divisibility properties of integers. In the present note we extend this classification to the infinite case. We prove that symplectic dual polar spaces and certain Hermitian dual polar spaces cannot have locally subquadrangular hyperplanes i...
متن کاملOn isometric full embeddings of symplectic dual polar spaces into Hermitian dual polar spaces
Let n ≥ 2, let K,K′ be fields such that K′ is a quadratic Galoisextension of K and let θ 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′, θ). We prove that the projective embedding of DW (2n − 1,K) induced by the Grassmann-embedding of DH(2n − 1,K′, θ) is ...
متن کاملUniform Hyperplanes of Finite Dual Polar Spaces of Rank 3
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 say that H is uniform. It is known that if H is locally singular, then either H is the set of poi...
متن کاملValuations and hyperplanes of dual polar spaces
Valuations were introduced in De Bruyn andVandecasteele (Valuations of near polygons, preprint, 2004) as a very important tool for classifying near polygons. In the present paperwe study valuations of dual polar spaces.Wewill introduce the class of theSDPS-valuations and characterize these valuations. We will show that a valuation of a finite thick dual polar space is the extension of an SDPS-v...
متن کاملOn a Class of Hyperplanes of the Symplectic and Hermitian Dual Polar Spaces
Let ∆ be a symplectic dual polar space DW (2n−1, K) or a Hermitian dual polar space DH(2n − 1, K, θ), n ≥ 2. We define a class of hyperplanes of ∆ arising from its Grassmann-embedding and discuss several properties of these hyperplanes. The construction of these hyperplanes allows us to prove that there exists an ovoid of the Hermitian dual polar space DH(2n−1, K, θ) arising from its Grassmann-...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2011
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.07.001