Uniform Hyperplanes of Finite Dual Polar Spaces of Rank 3

@article{Pasini2001UniformHO,
  title={Uniform Hyperplanes of Finite Dual Polar Spaces of Rank 3},
  author={Antonio Pasini and Sergey V. Shpectorov},
  journal={J. Comb. Theory, Ser. A},
  year={2001},
  volume={94},
  pages={276-288}
}
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… 
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