Skip to main content
SpringerLink
Log in

A combinatorial characterization of quadrics

  • Published:
Journal of Geometry Aims and scope Submit manuscript

Abstract

In this paper we prove that in a projective space of dimension three and orderq the two plane characterk-sets forkε {q 2+ 1,(q+1)2} are of the same type as the elliptic or the hyperbolic quadric, respectively. As a corollary we obtain a characterization of the elliptic and the hyperbolic quadrics.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A.Barlotti, Un'estensione del teorema di Segre-Kustaanheimo,Boll. Un. Mat. Ital. 10 (1955) 498–506.

    Google Scholar 

  2. A.Bichara, Suik-insiemi diS 3,q di tipo ((n−1)q+ 1,nq + l)2,Atti Accad. Naz. Lincei 62 (1977), 480–488.

    Google Scholar 

  3. P.Biondi,N.Melone, On sets of Plücker class two inPG(3,q),Annals of Discrete Math. 30 (1986), 99–104.

    Google Scholar 

  4. F.Buekenhout, Ensembles quadratiques des espaces projectifs,Math. Z. 110 (1969), 306–318.

    Google Scholar 

  5. F.Buekenhout,C.Lefèvre, Semi-quadratic sets in projective spaces,J. Geom. 7 (1976), 17–42.

    Google Scholar 

  6. J.W.P.Hirschfeld,Finite projective spaces of three dimensions, Clarendon Press Oxford 1985, 33–52.

    Google Scholar 

  7. G.Panella, Caratterizzazione delle quadriche di uno spazio (tridimensionale) lineare sopra un corpo finito,Boll. Un. Mat. Ital. 10 (1955) 507–513.

    Google Scholar 

  8. E.J.F.Primrose, Quadrics in finite geometries,Proc. Cambridge Philos. Soc. 47 (1951) 299–304.

    Google Scholar 

  9. D.K.Ray-Chaudhuri, Some results on quadrics in finite projective geometries based on Galois fields,Can. J. Math. 14 (1962), 129–138.

    Google Scholar 

  10. G.Tallini, Sullek-calotte di uno spazio lineare finito,Ann. Mat. 42 (1956), 119–164.

    Google Scholar 

  11. G.Tallini, Caratterizzazione grafica delle quadriche ellittiche negli spazi finiti,Rend. Mat. Appl. 16 (1957), 328–351.

    Google Scholar 

  12. M.Tallini Scafati, Suik-insiemi di uno spazio di GaloisS r,q a due soli caratteri nella dimensioned, Atti Accad. Naz. Lincei 40 (1976), 782–788.

    Google Scholar 

  13. M.Tallini Scafati, Thek-sets ofPG(r,q) from the character point of view,Finite Geometries C.A.Baker-L.M.Batteh Eds., Marcel Dekker Inc., New York 1985, 321–326.

    Google Scholar 

  14. J.A.Thas, A combinatorial problem,Geom. Dedicata 1 (1973), 236–240.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Universitá de L'Aquila, 1-67010, Coppito L'Aquila

    Osvaldo Ferri

  2. Italtel S.p.A., ss. 17 localitá Boschetto, I-67100, L'Aquila

    Stefania Ferri

  3. Dipartimento di Ingegneria Elettrica, Universitá de L'Aquila, I-67040, Monteluco di Roio L'Aquila

    Stefano Innamorati

Authors
  1. Osvaldo Ferri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefania Ferri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stefano Innamorati
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ferri, O., Ferri, S. & Innamorati, S. A combinatorial characterization of quadrics. J Geom 68, 81–86 (2000). https://doi.org/10.1007/BF01221063

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01221063

Keywords

Search

Navigation