Le groupe fondamental du complément d'une courbe plane n'ayant que des points doubles ordinaires est abélien

Pierre Deligne

Séminaire Bourbaki (1979-1980)

  • Volume: 22, page 1-10
  • ISSN: 0303-1179

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Deligne, Pierre. "Le groupe fondamental du complément d'une courbe plane n'ayant que des points doubles ordinaires est abélien." Séminaire Bourbaki 22 (1979-1980): 1-10. <http://eudml.org/doc/109954>.

@article{Deligne1979-1980,
author = {Deligne, Pierre},
journal = {Séminaire Bourbaki},
keywords = {complement to node curves; fundamental group; Zariski conjecture},
language = {fre},
pages = {1-10},
publisher = {Springer-Verlag},
title = {Le groupe fondamental du complément d'une courbe plane n'ayant que des points doubles ordinaires est abélien},
url = {http://eudml.org/doc/109954},
volume = {22},
year = {1979-1980},
}

TY - JOUR
AU - Deligne, Pierre
TI - Le groupe fondamental du complément d'une courbe plane n'ayant que des points doubles ordinaires est abélien
JO - Séminaire Bourbaki
PY - 1979-1980
PB - Springer-Verlag
VL - 22
SP - 1
EP - 10
LA - fre
KW - complement to node curves; fundamental group; Zariski conjecture
UR - http://eudml.org/doc/109954
ER -

References

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  1. [1] S. Abhyankar - Tame coverings and fundamental groups of algebraic varieties I , Amer. J. of Math., 81(1959), 46-94. Zbl0100.16401MR104675
  2. [2] D. Cheniot - Un théorème du type de Lefschetz, Annales de l'Institut Fourier, 251(1975), 195-213. Zbl0332.14007MR389909
  3. [2 bis] D. Cheniot - Une démonstration du théorème de Zariski sur les sections hyper-planes d'une hypersurface projective et du théorème de Van Kampen sur le groupe fondamental du complémentaire d'une courbe plane, Comp. Math., 272 (1973) , 141-158. Zbl0294.14010MR366922
  4. [3] W. Fulton - On the fundamental group of the complement of a node curve, Ann. of Math., 1112(1980), 407-409. Zbl0406.14008MR569076
  5. [4] W. Fulton and J. Hansen - A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings, Ann. of Math., 1091 (1979) , 159-166. Zbl0389.14002MR541334
  6. [5] T. Gaffney and R. Lazarsfeld - On the ramification of branched coverings of Pn , Inv. Math., 591(1980), 53-58. Zbl0422.14010MR575080
  7. [6] H. Hamm et Lê Dung Trang - Un théorème de Zariski du type de Lefschetz, Ann. Sci. E.N.S., 63(1973), 317-366. Zbl0276.14003MR401755
  8. [7] J.-P. Serre - Revêtements ramifiés du plan projectif (d'après S. Abhyankar), Sém. Bourbaki 204, mai 1960. Zbl0115.38403
  9. [8] O. Zariski - On the problem of existence of algebraic functions of two variables possessing a given branch curve, Amer. J. of Math., 51(1929), 305-328. Zbl55.0806.01MR1506719JFM55.0806.01
  10. [9] O. Zariski - Algebraic surfaces, second supplemented edition, Ergebnisse 61, Springer-Verlag. Zbl0219.14020MR469915
  11. Je viens (1/10/80) de recevoir un très bel exposé, faisant le point sur les méthodes étudiées ici, leurs variantes et leurs nombreuses applications : W. Fulton and R. Lazarsfeld - Connectivity and its applications in algebraic geometry. 

Citations in EuDML Documents

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  1. Nicholas M. Katz, A conjecture in the arithmetic theory of differential equations
  2. Madhav V. Nori, Zariski's conjecture and related problems
  3. Helmut A. Hamm, Lê Dũng Tráng, Lefschetz theorems on quasi-projective varieties
  4. Mario Salvetti, Arrangements of lines and monodromy of plane curves
  5. José Ignacio Cogolludo-Agustín, Braid Monodromy of Algebraic Curves
  6. G. Dethloff, M. Zaidenberg, Plane curves with hyperbolic and C -hyperbolic complements
  7. Michel Berthier, Dominique Cerveau, Quelques calculs de cohomologie relative
  8. François Loeser, Déformations de courbes planes

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