Deformations of coherent foliations on a compact normal space
Pourcin, Geneviève
Annales de l'Institut Fourier, Tome 37 (1987), p. 33-48 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

On munit d’une structure analytique universelle l’ensemble des feuilletages holomorphes sur un espace compact normal. Par définition un feuilletage holomorphe est un sous-faisceau cohérent du faisceau tangent holomorphe stable par le crochet de Lie.

An universal analytic structure is construted on the set of (singular) holomorphic foliations on a normal compact space. Such a foliation is by definition a coherent subsheaf of the holomorphic tangent sheaf stable by the Lie-bracket

@article{AIF_1987__37_2_33_0,
     author = {Pourcin, Genevi\`eve},
     title = {Deformations of coherent foliations on a compact normal space},
     journal = {Annales de l'Institut Fourier},
     volume = {37},
     year = {1987},
     pages = {33-48},
     doi = {10.5802/aif.1085},
     mrnumber = {88k:32057},
     zbl = {0587.32037},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1987__37_2_33_0}
}

Pourcin, Geneviève. Deformations of coherent foliations on a compact normal space. Annales de l'Institut Fourier, Tome 37 (1987) pp. 33-48. doi : 10.5802/aif.1085. http://gdmltest.u-ga.fr/item/AIF_1987__37_2_33_0/

[1] P. Baum, Structure of foliation singularities, Advances in Math., 15 (1975), 361-374. | MR 51 #13298 | Zbl 0296.57007

[2] G. Bohnhorst and H. J. Reiffen, Holomorphe blatterungen mit singularitäten, Math. Gottingensis, heft 5 (1985).

[3] H. Cartan, Faisceaux analytiques cohérents, C.I.M.E., Edizioni Cremonese, 1963. | Zbl 0178.42701

[4] A. Douady, Le problème des modules pour les sous-espaces analytiques..., Ann. Inst. Fourier, XVI, Fasc. 1 (1966), 1-96. | Numdam | Zbl 0146.31103

[5] B. Malgrange, Frobenius avec singularités-codimension 1, Pub I.H.E.S., n°46 (1976). | Numdam | MR 58 #22685a | Zbl 0355.32013

[6] G. Pourcin, Sous-espaces privilégiés d'un polycylindre, Ann. Inst. Fourier, XXV, Fasc. 1 (1975), 151-193. | Numdam | MR 52 #11118 | Zbl 0297.32010

[7] Y. T. Siu et G. Trautmann, Gap-sheaves and extension of coherent analytic subsheaves, Lect. Notes, 172 (1971). | MR 44 #4240 | Zbl 0208.10403

[8] T. Suwa, Singularities of complex analytic foliations, Proceedings of Symposia in Pure mathematics, Vol. 40 (1983), Part.2 | MR 85a:32029 | Zbl 0552.32008