On Semi-Pseudo-Ovoids
S. De Winter
and J.A. Thas
Department of Pure Mathematics and Computer Algebra Ghent University Krijgslaan 281-S22 B-9000 Gent Belgium
DOI: 10.1007/s10801-005-2510-6
Abstract
In this paper we introduce semi-pseudo-ovoids, as generalizations of the semi-ovals and semi-ovoids. Examples of these objects are particular classes of SPG-reguli and some classes of m-systems of polar spaces. As an application it is proved that the axioms of pseudo-ovoid O( n,2 n, q) in PG(4 n - 1, q) can be considerably weakened and further a useful and elegant characterization of SPG-reguli with the polar property is given.
Pages: 139–149
Keywords: keywords semi-pseudo-ovoid; egg; SPG-regulus; polar property
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References
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2. F. Buekenhout, “Characterizations of semi quadrics. A survey,” Colloquio Internazionale sulle Teorie Combinatorie (Roma, 1973), Tomo I, pp. 393-421. Atti dei Convegni Lincei, No. 17, Accad. Naz. Lincei, Rome, 1976.
3. R. Calderbank and W.K. Kantor, “The geometry of two-weight codes,” Bull. London Math. Soc. 18(2) (1986), 97-122.
4. S. De Winter and J.A. Thas, “SPG-reguli satisfying the polar property and a new semipartial geometry,” Des. Codes Cryptogr. 32 (2004), 153-166.
5. M. Lavrauw, “Scattered spaces with respect to spreads, and eggs in finite projective spaces,” Dissertation, Eindhoven University of Technology, Eindhoven, 2001, viii+115 pp.
6. D. Luyckx, “m-systems of polar spaces and SPG reguli,” Bull. Belg. Math. Soc. Simon Stevin 9(2) (2002), 177-183.
7. D. Luyckx and J.A. Thas, “Derivation of m-systems,” European J. Combin. 24(2) (2003), 137-147.
8. S.E. Payne, “An essay on skew translation generalized quadrangles,” Geom. Dedicata 32(1) (1989), 93-118.
9. S.E. Payne and J.A. Thas, Finite Generalized Quadrangles, Research Notes in Mathematics, vol. 110, Pitman Advanced Publishing Program, Boston, MA, 1984, vi+312 pp.
10. E.E. Shult and J.A. Thas, “m-systems of polar spaces,” J. Combin. Theory Ser. A 68(1) (1994), 184-204.
11. J.A. Thas, “On semi-ovals and semi-ovoids,” Geometriae Dedicata 3 (1974), 229-231.
12. J.A. Thas, “Semipartial geometries and spreads of classical polar spaces,” J. Combin. Theory Ser. A 35 (1983), 58-66.