Skip to main content
Log in

Two characterizations of the family of secant lines of an ovoid of PG(3, \({\varvec{q}}\))

  • Published:
Journal of Geometry Aims and scope Submit manuscript

Abstract

Two new characterizations of the family of secant lines to an ovoid of \(\mathrm {PG}(3, q)\) are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ball, S., Blokhuis, A., Mazzocca, F.: Maximal arcs in Desarguesian planes of odd order do not exist. Combinatorica 17, 31–41 (1997)

    Article  MathSciNet  Google Scholar 

  2. Barwick, S.G., Butler, D.K.: A characterisation of the lines external to an oval cone in PG(3, q), q even. J. Geom. 23, 21–27 (2009)

    Article  MathSciNet  Google Scholar 

  3. Durante, N., Olanda, D.: A characterization of the family of secant or external lines of an ovoid of PG(3, q). Bull. Belg. Math. Soc. 12, 1–4 (2005)

    MathSciNet  MATH  Google Scholar 

  4. Ferri, O., Tallini, G.: A characterization of the family of secant lines of an elliptic quadric in \({\rm PG}(3, q)\), \(q\) odd, Proceedings of the conference on combinatorial and incidence geometry: principles and applications (La Mendola, 1982). Rend. Sem. Mat. Brescia 7, 297–305 (1984)

  5. Hirschfeld, J.W.P.: Finite Projective Spaces of Three Dimensions. Oxford University Press, Oxford (1985)

    MATH  Google Scholar 

  6. Innamorati, S.: A characterization of the set of lines either external to or secant to an ovoid in PG(3, q). Australas. J. Comb. 49, 159–163 (2011)

    MathSciNet  MATH  Google Scholar 

  7. Thas, J.A.: On semiovals and semiovoids. Geom. Dedicata 3, 229–231 (1974)

    Google Scholar 

  8. Vasarelli, P.: A characterization of the external lines of a quadric cone in PG(3, q), q odd. J. Interdiscip. Math. 20, 1697–1706 (2017). https://doi.org/10.1080/09720502.2017.1367523

    Article  Google Scholar 

  9. Zannetti, M.: A characterization of the external lines of a hyperoval cone in PG(3, q), q even. Discrete Math. 311, 239–243 (2011)

    Article  MathSciNet  Google Scholar 

  10. Zuanni, F.: A characterization of the external lines of a hyperoval in in PG(3, q), q even. Discrete Math. 312, 1257–1259 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vito Napolitano.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This research was partially supported by G.N.S.A.G.A. of INdAM.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Napolitano, V. Two characterizations of the family of secant lines of an ovoid of PG(3, \({\varvec{q}}\)). J. Geom. 110, 21 (2019). https://doi.org/10.1007/s00022-019-0478-y

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1007/s00022-019-0478-y

Keywords

Mathematics Subject Classification

Navigation