manuscripta mathematica

, Volume 14, Issue 2, pp 163–172 | Cite as

The fundamental group of the complement of an algebraic curve

  • David Prill


A criterion of Abhyankar for abelianness of the fundamental group of the complement of an algebraic curve in the complex projective plane is proved in a refined form by different methods.


Number Theory Projective Plane Algebraic Geometry Fundamental Group Topological Group 
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  1. [1]
    Abhyankar, S. S.: Tame coverings and fundamental groups of algebraic varieties, Parts, I, II, III. American J. Math. 81, 46–94 (1959); 82, 120–178 (1960);82, 179–190 (1960).Google Scholar
  2. [2]
    —, Appendix 1 to Chapter VIII ofAlgebraic Surfaces by O. Zariski (Second supplemented edition). Ergebnisse der Math. und ihrer Grenzgebiete 61. Berlin-Heidelberg-New York: Springer 1971.Google Scholar
  3. [3]
    Cheniot, D.: Une démonstration du théorème de Zariski sur les sections hyperplanes d'une hypersurface projective et du théorème de van Kampen sur le groupe fondamental du complémentaire d'une courbe projective plane. Comp. Math. 27, 141–158 (1973).Google Scholar
  4. [4]
    —, and Lê Dung Tráng: Remarques sur les deux exposés précédents, in Singularités à Cargèse. Asterisque 7–8, 253–260 (1973).Google Scholar
  5. [5]
    Hirzebruch, F.: Über vierdimensionale Riemannsche Flächen mehrdeutiger analytischer Funktionen von zwei komplexen Veränderlichen. Math. Ann 126, 1–22 (1953).Google Scholar
  6. [6]
    Kodaira, K.: On compact complex analytic surfaces. Ann. Math. 71, 111–152 (1960).Google Scholar
  7. [7]
    Lazzeri, F.: A theorem on the monodromy of isolated singularities,in Singularités à Cargèse. Asterisque 7–8, 269–275 (1973).Google Scholar
  8. [8]
    Popp, H.: Fundamentalgruppen algebraischer Mannigfaltigkeiten. Lecture Notes No. 176. Berlin-Heidelberg-New York: Springer 1970.Google Scholar
  9. [9]
    —, Über die Fundamentalgruppe 2-dimensionaler schemata. Istituto nazionale die alta mathematica. Symposia mathematica vol. III, 403–451 (1970).Google Scholar
  10. [10]
    Serre, J.-P.: Revêtements ramifiés du plan projectif. Sém. Bourbaki 204 (1959/60).Google Scholar
  11. [11]
    van Kampen, E.: On the fundamental group of an algebraic curve. Amer. J. Math. 55, 255–260 (1933).Google Scholar
  12. [12]
    Zariski, O.: On the problem of existence of algebraic functions of two variables possessing a given branch curve. Amer. J. Math. 51, 305–328 (1929).Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • David Prill
    • 1
  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA

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