Israel Journal of Mathematics

, Volume 57, Issue 1, pp 107–115 | Cite as

On the distribution of Weierstrass points on singular curves

  • R. F. Lax


Weierstrass points are defined for invertible sheaves on integral, projective Gorenstein curves. An example is given of a rational nodal curveX and an invertible sheaf ℒ of positive degree onX such that the set of all higher order Weierstrass points of ℒ is not dense inX.


Line Bundle Smooth Point Linear Fractional Transformation Weierstrass Point Canonical Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Ju. Arakelov,Families of algebraic curves with fixed degeneracies, Izv. Akad. Nauk SSSR Ser. Mat.35 (1971), 1269–1293.MATHMathSciNetGoogle Scholar
  2. 2.
    S. Diaz,Exceptional Weierstrass points and the divisor on moduli space that they define, Mem. Amer. Math. Soc.56 (1985), no. 327.Google Scholar
  3. 3.
    H. Farkas and I. Kra,Riemann Surfaces, Springer-Verlag, New York, 1980.MATHGoogle Scholar
  4. 4.
    S. L. Kleiman,r-special subschemes and an argument of Severi’s, Advances in Math,22 (1976), 1–23.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    D. Laksov,Weierstrass points on curves, Astérisque87–88 (1981), 221–247.MathSciNetGoogle Scholar
  6. 6.
    D. Laksov,Wronskians and Plücker formulas for linear systems on curves, Ann. Sci. Éc. Norm. Sup.17 (1984), 45–66.MATHMathSciNetGoogle Scholar
  7. 7.
    R. F. Lax,Weierstrass points on rational nodal curves, Glasgow Math. J., to appear.Google Scholar
  8. 8.
    D. Mumford,Curves and their Jacobians, Univ. of Michigan Press, Ann Arbor, 1976.Google Scholar
  9. 9.
    D. Mumford,Tata lectures on theta II, Birkhäuser, Boston, 1983.Google Scholar
  10. 10.
    A. Neeman,The distribution of Weierstrass points on a compact Riemann surface, Ann. of Math.120 (1984), 317–328.CrossRefMathSciNetGoogle Scholar
  11. 11.
    R. Ogawa,On the points of Weierstrass in dimensions greater than one, Trans. Am. Math. Soc.184 (1973), 401–417.CrossRefMathSciNetGoogle Scholar
  12. 12.
    B. Olsen,On higher order Weierstrass points, Ann. of Math.95 (1972), 357–364.CrossRefMathSciNetGoogle Scholar
  13. 13.
    C. Widland,On Weierstrass points of Gorenstein curves, Ph.D. dissertation, Louisiana State University, 1984.Google Scholar

Copyright information

© The Weizmann Science Press of Israel 1987

Authors and Affiliations

  • R. F. Lax
    • 1
  1. 1.Department of MathematicsLouisiana State UniversityBaton RougeUSA

Personalised recommendations