Sur la densité des systèmes de Pfaff sans solution algébrique
Mendes, Luis G. ; Sebastiani, Marcos
Annales de l'Institut Fourier, Tome 44 (1994), p. 271-276 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

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.

@article{AIF_1994__44_1_271_0,
     author = {Mendes, Luis G. and Sebastiani, Marcos},
     title = {Sur la densit\'e des syst\`emes de Pfaff sans solution alg\'ebrique},
     journal = {Annales de l'Institut Fourier},
     volume = {44},
     year = {1994},
     pages = {271-276},
     doi = {10.5802/aif.1397},
     mrnumber = {95f:58008},
     zbl = {0792.58001},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1994__44_1_271_0}
}

Mendes, Luis G.; Sebastiani, Marcos. Sur la densité des systèmes de Pfaff sans solution algébrique. Annales de l'Institut Fourier, Tome 44 (1994) pp. 271-276. doi : 10.5802/aif.1397. http://gdmltest.u-ga.fr/item/AIF_1994__44_1_271_0/

[LN]A. Lins Neto, Construction of singular holomorphic vector fields and foliations in dimension two, J. Differential Geometry, 26 (1987), 1-31. | MR 88f:32047 | Zbl 0625.57012

[J]J.-P. Jouanolou, Equations de Pfaff algébriques, Lecture Notes in Math. Springer Verlag, vol. 708, 1979. | MR 81k:14008 | Zbl 0477.58002

[B]A. Beauville, Surfaces Algébriques Complexes, Astérisque, vol. 54 (1978). | MR 58 #5686 | Zbl 0394.14014

[C-S]C. Camacho et P. Sad, Invariant varieties through singularities of holomorphic vector fields, Ann. of Math., 115 (1982), 579-595. | MR 83m:58062 | Zbl 0503.32007