Integrals for holomorphic foliations with singularities having all leaves compact

Xavier Gomez-Mont

Annales de l'institut Fourier (1989)

  • Volume: 39, Issue: 2, page 451-458
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Gomez-Mont, Xavier. "Integrals for holomorphic foliations with singularities having all leaves compact." Annales de l'institut Fourier 39.2 (1989): 451-458. <http://eudml.org/doc/74837>.

@article{Gomez1989,
abstract = {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.},
author = {Gomez-Mont, Xavier},
journal = {Annales de l'institut Fourier},
keywords = {holomorphic foliation; quasiprojective},
language = {eng},
number = {2},
pages = {451-458},
publisher = {Association des Annales de l'Institut Fourier},
title = {Integrals for holomorphic foliations with singularities having all leaves compact},
url = {http://eudml.org/doc/74837},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Gomez-Mont, Xavier
TI - Integrals for holomorphic foliations with singularities having all leaves compact
JO - Annales de l'institut Fourier
PY - 1989
PB - Association des Annales de l'Institut Fourier
VL - 39
IS - 2
SP - 451
EP - 458
AB - 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.
LA - eng
KW - holomorphic foliation; quasiprojective
UR - http://eudml.org/doc/74837
ER -

References

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  2. [C.M.] D. CERVEAU, J.-F. MATTEI, Formes intégrables holomorphes singulières, Astérisque, 97 (1982). Zbl0545.32006MR86f:58006
  3. [E.M.S.] R. EDWARDS, K. MILLET, D. SULLIVAN, Foliations with all leaves compact, Topology, 16 (1977), 13-32. Zbl0356.57022MR55 #11268
  4. [E] D. EPSTEIN, Foliations with all leaves compact, Ann. Inst. Fourier, 26-1 (1976), 265-282. Zbl0313.57017MR54 #8664
  5. [F] A. FUJIKI, Closedness of the Douady spaces of compact Kaehler spaces, Publ. Math. RIMS, Kyoto U., 14 (1978). Zbl0409.32016MR58 #6361
  6. [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. Zbl0236.14003
  7. [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. Zbl0144.19904
  8. [H] R. HARTSHORNE, Algebraic Geometry, Springer Verlag, 1977. Zbl0367.14001MR57 #3116
  9. [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. Zbl0122.38603MR33 #7333
  10. [R] G. REEB, Sur certaines propriétés topologiques des variétés feuilletées, Actual. Scient. Ind., 1183 (1952). Zbl0049.12602MR14,1113a
  11. [Sh] I. SHAFAREVICH, Basic Algebraic Geometry, Springer Verlag, 1974. Zbl0284.14001MR51 #3163
  12. [S] G. STOLZENBERG, Volumes, Limits and Extensions of Analytic Varieties, LNM 19, Springer Verlag, 1966. Zbl0142.33801

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