Sur la densité des systèmes de Pfaff sans solution algébrique

Luis G. Mendes; Marcos Sebastiani

Annales de l'institut Fourier (1994)

  • Volume: 44, Issue: 1, page 271-276
  • ISSN: 0373-0956

Abstract

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It is proved that in every rational surface, non-isomorphic to the projective plane, there exists an holomorphic foliation which is rigid and has algebraic leaves, having only isolated singularities.

How to cite

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Mendes, Luis G., and Sebastiani, Marcos. "Sur la densité des systèmes de Pfaff sans solution algébrique." Annales de l'institut Fourier 44.1 (1994): 271-276. <http://eudml.org/doc/75058>.

@article{Mendes1994,
abstract = {On démontre que dans toute surface rationnelle, non-isomorphe au plan projectif, il existe une feuilletage analytique rigide, possédant des feuilles algébriques et n’ayant que des singularités isolées.},
author = {Mendes, Luis G., Sebastiani, Marcos},
journal = {Annales de l'institut Fourier},
keywords = {holomorphic foliations; projective rational surface},
language = {fre},
number = {1},
pages = {271-276},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sur la densité des systèmes de Pfaff sans solution algébrique},
url = {http://eudml.org/doc/75058},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Mendes, Luis G.
AU - Sebastiani, Marcos
TI - Sur la densité des systèmes de Pfaff sans solution algébrique
JO - Annales de l'institut Fourier
PY - 1994
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 1
SP - 271
EP - 276
AB - On démontre que dans toute surface rationnelle, non-isomorphe au plan projectif, il existe une feuilletage analytique rigide, possédant des feuilles algébriques et n’ayant que des singularités isolées.
LA - fre
KW - holomorphic foliations; projective rational surface
UR - http://eudml.org/doc/75058
ER -

References

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  1. [LN]A. LINS NETO, Construction of singular holomorphic vector fields and foliations in dimension two, J. Differential Geometry, 26 (1987), 1-31. Zbl0625.57012MR88f:32047
  2. [J]J.-P. JOUANOLOU, Equations de Pfaff algébriques, Lecture Notes in Math. Springer Verlag, vol. 708, 1979. Zbl0477.58002MR81k:14008
  3. [B]A. BEAUVILLE, Surfaces Algébriques Complexes, Astérisque, vol. 54 (1978). Zbl0394.14014MR58 #5686
  4. [C-S]C. CAMACHO et P. SAD, Invariant varieties through singularities of holomorphic vector fields, Ann. of Math., 115 (1982), 579-595. Zbl0503.32007MR83m:58062

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