Valuations and hyperplanes of dual polar spaces
نویسندگان
چکیده
منابع مشابه
Valuations 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 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 کاملLocally 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 extensions of hyperplanes of dual polar spaces
Let ∆ be a thick dual polar space and F a convex subspace of diameter at least 2 of ∆. Every hyperplane G of the subgeometry F̃ of ∆ induced on F will give rise to a hyperplane H of ∆, the so-called extension of G. We show that F and G are in some sense uniquely determined by H. We also consider the following problem: if e is a full projective embedding of ∆ and if eF is the full embedding of F̃ ...
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: Journal of Combinatorial Theory, Series A
سال: 2005
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2005.02.001