Ovoids and spreads of the generalized hexagon H(3)

In this paper, 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 typ...

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Bibliographic Details
Published inDiscrete mathematics Vol. 305; no. 1; pp. 299 - 311
Main Authors De Wispelaere, A., Huizinga, J., Van Maldeghem, H.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 06.12.2005
Elsevier
Subjects
Combinatorics
Combinatorics. Ordered structures
Designs and configurations
Exact sciences and technology
GAB
Generalized hexagon
Mathematics
Ovoids
Sciences and techniques of general use
Spread
Ovoids
GAB
Spread
Generalized hexagon
Construction
Ovoid
Spreading
Ovoids: Spread
Pairing
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Summary:In this paper, 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 G ˜ 2 . We also exhibit new ovoid-spread pairings.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2005.10.004