Uniform Hyperplanes of Finite Dual Polar Spaces of Rank 3

  title={Uniform Hyperplanes of Finite Dual Polar Spaces of Rank 3},
  author={Antonio Pasini and Sergey V. Shpectorov},
  journal={J. Comb. Theory, Ser. A},
Let ? be a finite thick dual polar space of rank 3. We say that a hyperplane H of ? 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 ?. 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 points at non-maximal distance from a given point of ? or ? is the dual of Q(6, q) and H arises from the… 
Certain generalized quadrangles inside polar spaces of rank 4
Let ∆ be the dual of a thick polar space Π of rank 4. The points, lines, quads, and hexes of ∆ correspond with the singular 3-spaces, planes, lines, respectively points of Π. Pralle and Shpectorov
A Remark on Non-Uniform Hyperplanes of Finite Thick Dual Polar Spaces
It is proved that each non-uniform hyperplane H of a finite thick dual polar space meets some quad in the perp of a point.
Non-Classical Hyperplanes of Finite Thick Dual Polar Spaces
  • B. Bruyn
  • Mathematics
    Electron. J. Comb.
  • 2018
In view of the absence of known examples of ovoids and semi-singular hyperplanes in finite thick dual polar spaces of rank 3, the condition on the nonexistence of these hex intersections can be regarded as not very restrictive.
A characterization of a class of hyperplanes of DW(2n-1, F)
The hyperplanes of DW(5, 2h) which arise from embedding
Points and hyperplanes of the universal embedding space of the dual polar space DW(5,q), q odd
It was proved earlier that there are 6 isomorphism classes of hyperplanes in the dual polar space (5,q)$, $ even, which arise from its Grassmann-embedding. In the present paper, we extend these
Non-Classical Hyperplanes of DW(5, q)
  • B. Bruyn
  • Mathematics
    Electron. J. Comb.
  • 2013
If $q$ is even, then it is proved that every non-classical ovoid of DW(5,q) is either a semi-singular hyperplane or the extension of a non- classical o void of a quad of $DW(5-q)$.
On the simple connectedness of hyperplane complements in dual polar spaces


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Extending Polar Spaces of Rank at Least 3
Generalized hexagons as geometric hyperplanes of near hexagons, in ``Groups, Combinatorics and Geometry'' (M
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