On the Twisted Cubic of PG(3, q)
G. Lunardon
and O. Polverino
DOI: 10.1023/B:JACO.0000011940.77655.b4
Abstract
In this paper we classify the lines of PG(3, q) whose points belong to imaginary chords of the twisted cubic of PG(3, q). Relying on this classification result, we obtain a complete classification of semiclassical spreads of the generalized hexagon H( q).
Pages: 255–262
Keywords: twisted cubics; generalized hexagons; coset geometries; spreads
Full Text: PDF
References
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2. L. Bader and G. Lunardon, “Generalized hexagons and polar spaces,” Discrete Math. 208/209 (1999), 13-22.
3. I. Bloemen, J.A. Thas, and H. Van Maldeghem, “Translation ovoids of generalized quadrangles and hexagons,” Geom. Dedicata 72 (1998), 19-62.
4. A.A. Bruen and J.W.P. Hirschfeld, “Applications of line geometry over finite fields I: The twisted cubic,” Geom. Dedicata 6 (1977), 495-509.
5. P.J. Cameron, S.E. Payne, and J.A. Thas, “Polarities of generalized hexagons and perfect codes,” Geom. Dedicata, 5 (1976), 525-528.
6. I. Cardinali, G. Lunardon, O. Polverino, and R. Trombetti,” Spreads in H (q) and 1-systems of Q(6, q),” European J. Combin., 23 (2002), 367-376.
7. J.W.P. Hirschfeld, Finite Projective Spaces of Three Dimensions. The Clarendon Press Oxford University Press, New York, 1985.
8. D. Luyckx and J.A. Thas, “On 1-systems of Q(6, q), q even,” preprint.
9. A.D. Offer, “Translation spreads of the split Cayley hexagon,” Advances in Geometry, 3(2) (2003), 105-121.
10. H. Stichtenoth, Algebraic Function Fields and Codes, Springer-Verlag, 1993.
11. J. Tits, Sur la trialité et certains groupes qui s'en déduisent, Inst. Hautes Études Sci. Publ. Math. 2 (1959), 14-60.
12. H. Van Maldeghem, Generalized Polygons, Monographs in Mathematics, Vol. 93, Birkh\ddot auser Verlag, Basel, 1998.