Skip to main content
SpringerLink
Log in

Semi — Quadratic sets in projective spaces

  • Published:
Journal of Geometry Aims and scope Submit manuscript

Abstract

The purpose of this paper is to characterize semi-quadrics in projective spacesP of finite dimension 2 at least. A concept of semi-quadratic set inP is introduced: a semi-quadratic setQ inP is essentially a set of points ofP such that the union of all tangent lines at each pointp ofQ is either a hyperplane ofP orP itself. (A tangent line ofQ atp is a line contained inQ or meetingQ exactly inp). The main result is that a semi-quadratic set which is invariant under “many” perspectivities is a semi-quadric.

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

    Google Scholar 

  2. - Characterizations of semi-quadrics: a survey. To appear in Atti Colloq.Teo.Combin. Roma.

  3. - On weakly perspective subsets of desarguesian projective lines. To appear in Abh. Math.Sem.Hamburg.

  4. - The structure of semi-quadrics in projective spaces. (To appear).

  5. BUEKENHOUT, F. and LEFEVRE, C. Generalized quadrangles in projective spaces. To appear in Archiv.der Math.

  6. BUEKENHOUT, F. and SHULT, E. On the foundation of polar geometry. Geom.Ded. 3 (1974), 155–170.

    Google Scholar 

  7. TITS, J. Buildings and BN-pairs of spherical type. Berlin-Springer Verlag 1974.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Free University of Brussels, Avenue F.D.Roosevelt 50, B-1050, Bruxelles, Belgium

    Francis Buekenhout & Christiane Lefèvre

Authors
  1. Francis Buekenhout
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christiane Lefèvre
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Aspirant au Fonds National de la Recherche Scientifique de Belgique.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buekenhout, F., Lefèvre, C. Semi — Quadratic sets in projective spaces. J Geom 7, 17–42 (1976). https://doi.org/10.1007/BF01918304

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01918304

Keywords

Search

Navigation