Translation Ovoids of Generalized Quadrangles and Hexagnos

@article{Bloemen1998TranslationOO,
  title={Translation Ovoids of Generalized Quadrangles and Hexagnos},
  author={I. Bloemen and Joseph A. Thas and Hendrik Van Maldeghem},
  journal={Geometriae Dedicata},
  year={1998},
  volume={72},
  pages={19-62}
}
We define the notion of a translation ovoid in the classical generalized quadrangles and hexagons of order q, and we enumerate all known examples; translation spreads are defined dually. A modification of the known ovoids in the generalized hexagon H(q), q=32h+1, yields new ovoids of that hexagon. Dualizing and projecting along reguli, we obtain an alternative construction of the Roman ovoids due to Thas and Payne. Also, we construct a new translation spread in H(q) for any ≡ 1 mod 3, q odd… CONTINUE READING

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