Abstract
One can define holomorphic foliations with singularities on a reduced complex space X as a coherent subsheaf T of the tangent sheaf HX stable by the bracket of derivations ([B],[G-M],[P2],[S]) or as a coherent subsheaf Ω of the sheaf of holomorphic 1-forms satisfying an integrability condition ([R],[Su]).
If X is compact the set of all the(singular) foliations on X has an universal analytic structure associated to each definition (vector fields or differential forms); these analytic structures are different but coincide on the open subset of regular foliations.
Moreover one obtains a semi-universal simultaneous deformation of a compact manifold and its foliations.
I thank H.J.REIFFEN, X. GOMEZ-MONT and H.FLENNER for usefull discussions.
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Bibliography
P. BAUM "Structure of foliations singularities" Adv. in Math. 15(1975)
H. CARTAN "Faisceaux analytiques coherents" C.I.M.E.(1963)Ed.Cremonese
A. DOUADY "Le problème des modules pour les sous-espaces …" Ann.Inst. Fourier, 16, (1966), 1–95
A. DOUADY "Le problème des modules locaux.." Ann.Sc. ENS, 7,(1974) 569–602
J. FRISCH "Aplatissement en géométrie analytique" Ann.SC.Norm.Sup. PISA, 1,(1968),305–312
J. GIRBAU-A. HAEFLIGER-D. SUNDARARAMAN "On deformations of transversally holomorphic foliations" J.Reine u.Ang.Math., 345, (1983), 122–147
X. GOMEZ-MONT "The transverse dynamics of a holomorphic flow" Pré-Pub.UNAM MEXICO,(1986)
H.GRAUERT-R.REMMERT "Analytische Stellenalgebren"(Springer 1971)
M. KURANISHI "On the locally complete families of complex analytic structures"Ann.of Math., 75,(1962),536–577
G. POURCIN "Théorème de Douady au-desssus de S"Ann.Sc.Norm.Sup.PISA XXIII,(1969),451–459
G. POURCIN "Deformations of coherent foliations on a compact normal space" Ann.Inst.Fourier, 2,t.37,(1987) (à paraître)
H.J.REIFFEN "The variety of moduli of foliations on a compactcomplex space" Pub.Universität OSNABRUCK, (1986)
K. SAITO "On a generalization of de Rham lemma" Ann.Inst.Fourier XXVI,(1976),2,165–170
T. SUWA "Unfoldings of complex analytic foliations with singularities" Japan.J. Math., 9,1,(1983),181–206.
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© 1988 Springer-Verlag
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Pourcin, G. (1988). Deformations of singular holomorphic foliations on reduced compact ℂ-analytic spaces. In: Gomez-Mont, X., Seade, J.A., Verjovski, A. (eds) Holomorphic Dynamics. Lecture Notes in Mathematics, vol 1345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081405
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DOI: https://doi.org/10.1007/BFb0081405
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