Abstract
Ovoids of the finite classical generalized hexagon H(q) that are translation with respect to a point are classified. By duality, translation spreads with respect to a line are classified when the characteristic is three. When the characteristic is not equal to three, it is shown that there are no ovoids that are translation with respect to a flag.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bloemen, I., Thas, J. A. and van Maldeghem, H.: Translation ovoids of generalized quadrangles and hexagons, Geom. Dedicata 72 (1998), 19–62.
Carlitz, L.: A theorem on `ordered' polynomials in a finite field, Acta Arith. 7 (1962), 167–172.
De Smet, V. and van Maldeghem, H.: The finite Moufang hexagons coordinatized, Beit. Algebra Geom. 34 (1993), 217–232.
Hirschfeld, J. W. P.: Finite Projective Spaces of Three Dimensions, Oxford Univ. Press, Oxford, 1985.
Hirschfeld, J. W. P.: Projective Geometries over Finite Fields, 2nd edn, Oxford Univ. Press, Oxford, 1988.
Hirschfeld, J. W. P. and Thas, J. A.: General Galois Geometries, Oxford Univ. Press, Oxford, 1995.
Maldeghem, H. van: Generalized Polygons, Monogr. in Math. 93, Birkhäuser, Basel, 1998.
O'Keefe, C. M. and Thas, J. A.: Ovoids of the quadric Q(2n, q), European J. Combin. 16 (1995), 87–92.
Thas, J. A.: Polar spaces, generalized hexagons and perfect codes, J. Combin. Theory Ser. A 29 (1980), 87–93.
Thas, J. A.: Ovoids and spreads of finite classical polar spaces, Geom. Dedicata 10 (1981), 135–144.
Tits, J.: Sur la trialité et certains groupes qui s'en déduisent, Inst. Hautes Études Sci. Publ. Math. 2 (1959), 14–60.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Offer, A. Translation Ovoids and Spreads of the Generalized Hexagon H(q). Geometriae Dedicata 85, 135–145 (2001). https://doi.org/10.1023/A:1010389603838
Issue Date:
DOI: https://doi.org/10.1023/A:1010389603838