Partial Flocks of Quadratic Cones with a Point Vertex in Pg (n,q), n Odd
Christine M. O'Keefe
and J.A. Thas
DOI: 10.1023/A:1008677211380
Abstract
We generalise the definition and many properties of flocks ofquadratic cones in PG (3,q) to partial flocks of quadratic coneswith vertex a point in PG (p,q), for n 
3 odd.
3 odd.Pages: 377–392
Keywords: Galois geometry; flock; cone; ovoid; cap
Full Text: PDF
References
1. L. Bader, G. Lunardon, and J.A. Thas, “Derivation of flocks of quadratic cones,” Forum Math. 2 (1990), 163-174.
2. W.E. Cherowitzo, T. Penttila, I. Pinneri, and G.F. Royle, “Flocks and ovals,” Geom. Dedicata 60 (1996), 17-37.
3. J.C. Fisher and J.A. Thas, “Flocks in PG(3, q),” Math. Z. 169 (1979), 1-11.
4. J.W.P. Hirschfeld, Projective Geometries Over Finite Fields, Oxford University Press, Oxford, 1979.
5. J.W.P. Hirschfeld, Finite Projective Spaces of Three Dimensions, Oxford University Press, Oxford, 1985.
6. J.W.P. Hirschfeld and J.A. Thas, “Sets of type (1, n, q + 1) in PG(d, q),” Proc. London Math. Soc. (3) 41 (1980), 254-278.
7. J.W.P. Hirschfeld and J.A. Thas, “The characterization of projections of quadrics over finite fields of even order,” J. London Math. Soc. (2) 22 (1980), 226-238.
8. J.W.P. Hirschfeld and J.A. Thas, General Galois Geometries, Oxford University Press, Oxford, 1991.
9. W.M. Kantor, “Ovoids and translation planes,” Canad. J. Math. 34 (1982), 1195-1207.
10. S.E. Payne and J.A. Thas, Finite Generalized Quadrangles, Pitman, London, 1984.
11. L. Storme and J.A. Thas, “k-arcs and partial flocks,” Linear Algebra and Its Applications 226-228 (1995), 33-45.
12. J.A. Thas, “Generalized quadrangles and flocks of cones,” European J. Combin. 8 (1987), 441-452.
13. M. Walker, “A class of translation planes,” Geometriae Dedicata 5 (1976), 135-146.
2. W.E. Cherowitzo, T. Penttila, I. Pinneri, and G.F. Royle, “Flocks and ovals,” Geom. Dedicata 60 (1996), 17-37.
3. J.C. Fisher and J.A. Thas, “Flocks in PG(3, q),” Math. Z. 169 (1979), 1-11.
4. J.W.P. Hirschfeld, Projective Geometries Over Finite Fields, Oxford University Press, Oxford, 1979.
5. J.W.P. Hirschfeld, Finite Projective Spaces of Three Dimensions, Oxford University Press, Oxford, 1985.
6. J.W.P. Hirschfeld and J.A. Thas, “Sets of type (1, n, q + 1) in PG(d, q),” Proc. London Math. Soc. (3) 41 (1980), 254-278.
7. J.W.P. Hirschfeld and J.A. Thas, “The characterization of projections of quadrics over finite fields of even order,” J. London Math. Soc. (2) 22 (1980), 226-238.
8. J.W.P. Hirschfeld and J.A. Thas, General Galois Geometries, Oxford University Press, Oxford, 1991.
9. W.M. Kantor, “Ovoids and translation planes,” Canad. J. Math. 34 (1982), 1195-1207.
10. S.E. Payne and J.A. Thas, Finite Generalized Quadrangles, Pitman, London, 1984.
11. L. Storme and J.A. Thas, “k-arcs and partial flocks,” Linear Algebra and Its Applications 226-228 (1995), 33-45.
12. J.A. Thas, “Generalized quadrangles and flocks of cones,” European J. Combin. 8 (1987), 441-452.
13. M. Walker, “A class of translation planes,” Geometriae Dedicata 5 (1976), 135-146.