Integrals for holomorphic foliations with singularities having all leaves compact
Annales de l'Institut Fourier, Volume 39 (1989) no. 2, pp. 451-458.

We show that for a holomorphic foliation with singularities in a projective variety such that every leaf is quasiprojective, the set of rational functions that are constant on the leaves form a field whose transcendence degree equals the codimension of the foliation.

Nous démontrons que pour un feuilletage holomorphe avec singularités dans une variété projective tel que toute feuille est quasi-projective, l’ensemble des fonctions rationnelles qui sont constantes sur les feuilles forment un champ dont le degré de transcendance est la codimension du feuilletage.

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     author = {Gomez-Mont, Xavier},
     title = {Integrals for holomorphic foliations with singularities having all leaves compact},
     journal = {Annales de l'Institut Fourier},
     pages = {451--458},
     publisher = {Institut Fourier},
     volume = {39},
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     year = {1989},
     doi = {10.5802/aif.1173},
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     url = {http://archive.numdam.org/articles/10.5802/aif.1173/}
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Gomez-Mont, Xavier. Integrals for holomorphic foliations with singularities having all leaves compact. Annales de l'Institut Fourier, Volume 39 (1989) no. 2, pp. 451-458. doi : 10.5802/aif.1173. http://archive.numdam.org/articles/10.5802/aif.1173/

[D] A. Douady, Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Ann. Inst. Fourier, 16-1 (1966), 1-95. | EuDML | Numdam | MR | Zbl

[C.M.] D. Cerveau, J.-F. Mattei, Formes intégrables holomorphes singulières, Astérisque, 97 (1982). | MR | Zbl

[E.M.S.] R. Edwards, K. Millet, D. Sullivan, Foliations with all leaves compact, Topology, 16 (1977), 13-32. | MR | Zbl

[E] D. Epstein, Foliations with all leaves compact, Ann. Inst. Fourier, 26-1 (1976), 265-282. | EuDML | Numdam | MR | Zbl

[F] A. Fujiki, Closedness of the Douady spaces of compact Kaehler spaces, Publ. Math. RIMS, Kyoto U., 14 (1978). | MR | Zbl

[G] A. Grothendieck, Techniques de construction et théorèmes d'existence en Géométrie Algébrique IV : Les Schémas de Hilbert, Séminaire Bourbaki, Exp. 221 (1961), Benjamin, N.Y., 1975. | EuDML | Numdam | Zbl

[G.D.] A. Grothendieck, J. Dieudonné, Éléments de Géométrie Algébrique IV : Étude locale des schémas et de morphismes de schémas, Publ. Math. IHES, 28, 1966. | EuDML | Numdam | Zbl

[H] R. Hartshorne, Algebraic Geometry, Springer Verlag, 1977. | MR | Zbl

[Hi] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, Annals of Math., 79 (1964), I : 109-203 ; II : 205-326. | MR | Zbl

[R] G. Reeb, Sur certaines propriétés topologiques des variétés feuilletées, Actual. Scient. Ind., 1183 (1952). | MR | Zbl

[Sh] I. Shafarevich, Basic Algebraic Geometry, Springer Verlag, 1974. | MR | Zbl

[S] G. Stolzenberg, Volumes, Limits and Extensions of Analytic Varieties, LNM 19, Springer Verlag, 1966. | Zbl

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