Ovoids and spreads of the generalized hexagon \(\mathbf H(3)\). (English) Zbl 1120.51004
Summary: We construct and classify all ovoids and spreads of the known generalized hexagon of order 3 (the split Cayley hexagon \(H(3))\). We exhibit some unexpected and nice geometric properties. As an application, we provide an elementary and geometric construction of a \(G_2(3)\)-GAB of type \(\widetilde G_2\). We also exhibit new ovoid-spread pairings.
MSC:
| 51E12 | Generalized quadrangles and generalized polygons in finite geometry |
References:
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