Name
Abstract | ||
|---|---|---|
Let Δ be a finite thick dual polar space of rank 3. We say that a hyperplane H of Δ 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 Δ . 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 Δ or Δ is the dual of Q (6, q ) and H arises from the generalized hexagon H ( q ). In this paper we prove that only two examples exist for the locally quadrangular case, arising in Q (6, 2) and H (5, 4), respectively. We fail to rule out the locally ovoidal case, but we obtain some partial results on it, which imply that, in this case, the geometry Δ \ H induced by Δ on the complement of H cannot be flag-transitive. As a bi-product, the hyperplanes H with Δ \ H flag-transitive are classified. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1006/jcta.2000.3136 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
uniform hyperplanes,finite dual polar space | Combinatorics,Ovoid,Polar,Polar space,Hyperplane,Mathematics | Journal |
Volume | Issue | ISSN |
94 | 2 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
19 | 4.45 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| A. Pasini | 1 | 19 | 4.45 |
| S. Shpectorov | 2 | 82 | 15.28 |