Skip to main content
SpringerLink
Log in

A combinatorial characterization of the Klein quadric

  • Published:
Journal of Geometry Aims and scope Submit manuscript

Abstract

We give a combinatorial characterization of the Klein quadric in terms of its incidence structure of points and lines. As an application, we obtain a combinatorial proof of a result of Havlicek.

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. BARLOTTI, A.:Un'estensione del Theorem di Segre — Kustaanheimo, Boll. Un. Mat. It.,10, (1955), 498–506.

    Google Scholar 

  2. BUEKENHOUT, F.:Ensembles quadratiques des espaces projectifs. Math. Z.,110, (1969), 306–318.

    Google Scholar 

  3. BUEKENHOUT, F. and LEFEVRE, C.:Semi-quadratic sets inprojective spaces, J.Geom.,7, (1976), 17–42.

    Google Scholar 

  4. HAVLICEK, H.:ZurTheorie linearer abbildungen I, II, J. Geom.,16, (1981), 152–180.

    Google Scholar 

  5. LEFEVRE, C.:Tallini sets in projective spaces, Atti Accad. Naz. Lincei Rend. Sc. Fis. Mat. e Nat.,59, (1975), 392–400.

    Google Scholar 

  6. PANELLA, G.:Caratterizzazione delle quadriche di uno spazio (tridimensionale) lineare sopra un corpo finito, Boll. Un. Mat. It.,10, (1955), 507–515.

    Google Scholar 

  7. TALLINI, G.:Sulle k-calotte di uno spazio lineare finito, Ann. Mat. Pura Appl.,42, (1956), 119–164.

    Google Scholar 

  8. TALLINI, G.:Caratterizzazione grafica delle quadriche ellittiche negli spazi finiti, Rend. Mat. e Appl.,16, (1957), 328–351.

    Google Scholar 

  9. Tallini, G.:Graphic characterization of algebraic varieties in a Galois space, Atti Colloq. Internaz. Teorie Comb., (Roma, 3,15 sett. 1973). Tomo II, Acc. Naz. Lincei, (1976), 153–165.

Download references

Author information

Authors and Affiliations

  1. Dip. Mat. ed Appl. “ R. Caccioppoli ”, Università di Napoli “ Federico II ”, Via Cintia-Compl. Monte Sant' Angelo, 80126, Napoli, Italia

    Eva Ferrara Dentice & Pia Maria Lo Re

  2. Istituto di Matematica, Seconda Univ. degli Studi di Napoli, Piazza Duomo, 81100, Caserta, Italia

    Nicola Melone

Authors
  1. Eva Ferrara Dentice
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pia Maria Lo Re
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicola Melone
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

In memoriam Giuseppe Tallini

Work supported by National Research Project “ Strutture Geometriche, Combinatoria e loro applicazioni ” of the Italian “ Ministere dell'Università e della Ricerca Scientifica ” and by “ G.N.S.A.G.A. ” of “ C.N.R. ”

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dentice, E.F., Lo Re, P.M. & Melone, N. A combinatorial characterization of the Klein quadric. J Geom 57, 106–113 (1996). https://doi.org/10.1007/BF01229255

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01229255

Keywords

Search

Navigation