Hyperplanes of DW(5, K) containing a quad
نویسنده
چکیده
We prove that every hyperplane of the symplectic dual polar space DW (5, K) that contains a quad is either classical or the extension of a non-classical ovoid of a quad of DW (5, K).
منابع مشابه
Non-Classical Hyperplanes of DW(5, q)
The hyperplanes of the symplectic dual polar space DW (5, q) arising from embedding, the so-called classical hyperplanes of DW (5, q), have been determined earlier in the literature. In the present paper, we classify non-classical hyperplanes of DW (5, q). If q is even, then we prove that every such hyperplane is the extension of a non-classical ovoid of a quad of DW (5, q). If q is odd, then w...
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Let F and F′ be two fields such that F′ is a quadratic Galois extension of F. If |F| ≥ 3, then we provide sufficient conditions for a hyperplane of the Hermitian dual polar space DH(5,F′) to arise from the Grassmann embedding. We use this to give an alternative proof for the fact that all hyperplanes of DH(5, q2), q 6= 2, arise from the Grassmann embedding, and to show that every hyperplane of ...
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Let K be a perfect field of characteristic 2. In this paper, we classify all hyperplanes of the symplectic dual polar space DW(5,K) that arise from its Grassmann embedding. We show that the number of isomorphism classes of such hyperplanes is equal to 5+N , where N is the number of equivalence classes of the following equivalence relation R on the set {λ ∈ K |X2 + λX + 1 is irreducible in K[X]}...
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Let K be a perfect field of characteristic 2. In this paper, we classify all hyperplanes of the symplectic dual polar space DW (5,K) that arise from its Grassmann embedding. We show that the number of isomorphism classes of such hyperplanes is equal to 5 + N , where N is the number of equivalence classes of the following equivalence relation R on the set {λ ∈ K |X2 + λX + 1 is irreducible in K[...
متن کاملThe hyperplanes of DW(5,F) arising from the Grassmann embedding
The hyperplanes of the symplectic dual polar space DW (5,F) that arise from the Grassmann embedding have been classified in [B.N. Cooperstein and B. De Bruyn. Points and hyperplanes of the universal embedding space of the dual polar space DW (5, q), q odd. Michigan Math. J., 58:195–212, 2009.] in case F is a finite field of odd characteristic, and in [B. De Bruyn. Hyperplanes of DW (5,K) with K...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 313 شماره
صفحات -
تاریخ انتشار 2013