Results in Mathematics

, Volume 46, Issue 1–2, pp 13–15 | Cite as

Common Ramification Points of Pencils on Double Covering Curves

  • E. Ballico
  • C. Keem


Let f: X → C be a “ general ” double covering of a smooth curve C of genus h ≥ 1. Here we show (with some restrictions on C if h ≥ 2) that there is no PX which is a common ramification point of all degree \({cal G} - 2h + 1\) morphisms X → P1.

MSC (2000)

14H45 14H51 

Key words

bielliptic curve double covering h-hyperelliptic curve ramification point 


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  1. [1]
    E. Ballico and C. Keem, On multiple coverings of irrational curves, Arch. Math. (Basel) 65 (1995), no. 2, 151–160.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    E. Ballico and C. Keem, Variety of linear systems on double covering curves, J. Pure Appl. Algebra 128 (1998), no. 3, 213–224.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    M. Coppens, C. Keem and G. Martens, Primitive linear series on curves, Manuscripta Math. 77 (1992), 237–264.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    E. Kani, On Castelnuovo’s equivalence defect, J. Reine Angew. Math. 352 (1984), 24–70.MathSciNetMATHGoogle Scholar
  5. [5]
    D. Perrin, Courbes passant par m points généraux de P3, Mem. Soc. Math. France n. 28/29, 1987.Google Scholar

Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TrentoPovo (TN)Italy
  2. 2.Department of MathematicsSeoul National UniversitySeoulSouth Korea

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