# 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…

## 35 Citations

Certain generalized quadrangles inside polar spaces of rank 4

- Mathematics
- 2006

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

- Mathematics, GeologyEur. J. Comb.
- 2001

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

- MathematicsElectron. 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.

The simple connectedness of hyperplane complements in thick dual polar spaces of rank at least 4

- MathematicsElectron. Notes Discret. Math.
- 2006

Points and hyperplanes of the universal embedding space of the dual polar space DW(5,q), q odd

- Mathematics
- 2009

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)

- MathematicsElectron. 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

- MathematicsDiscret. Math.
- 2009

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