Designs, Codes and Cryptography

, Volume 57, Issue 3, pp 347–360 | Cite as

On the intersection of a Hermitian curve with a conic



Let \({\mathcal{H}}\) be a Hermitian curve and let Γ be a conic of PG(2, q 2). In this paper we determine the possible intersection configurations between Γ and \({\mathcal{H}}\) under the hypotheses that Γ and \({\mathcal{H}}\) either share two points with the same tangent lines or contain a common Baer subconic. Moreover, the intersection configurations between a degenerate Hermitian curve and a conic sharing a Baer subconic are also determined.


Hermitian curve Conic Baer subconic 

Mathematics Subject Classification (2000)

51E20 05B25 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Coxeter H.S.M.: Projective Geometry, 2nd edn. University of Toronto Press, Toronto (1974)MATHGoogle Scholar
  2. 2.
    Donati G., Durante N.: Baer subplanes generated by collineations between pencils of lines. Rend. Circ. Mat. Palermo 54(2), Tomo LIV (2005), no. 1, 93–100.Google Scholar
  3. 3.
    Hirschfeld J.W.P.: Projective geometries over finite fields. Oxford Mathematical Monographs, Clarendon Press, Oxford (1979)MATHGoogle Scholar
  4. 4.
    Hirschfeld J.W.P., Thas J.A.: General Galois Geometries. Oxford University Press, Oxford (1991)MATHGoogle Scholar
  5. 5.
    Segre B.: Forme e geometrie hermitiane con particolare riguardo al caso finito. Ann. Mat. Pura Appl. 70, 1–201 (1965)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Semple J.G., Kneebone G.T.: Algebraic Projective Geometry. Oxford University Press, Oxford (1952)MATHGoogle Scholar
  7. 7.
    Steiner J.: Systematische Entwicklung der Abhängigkeit geometrischer Gestalten von einander. Reimer, Berlin (1832)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di Napoli “Federico II”NapoliItaly

Personalised recommendations