Abstract
After a brief discussion of holomorphic and transversely holomorphic nonsingular foliations the authors concentrate on constructing versal space of deformations of a holomorphic foliation with singularities in a compact manifold and describe a homological method to construct the tangent space to the versal space. Finally holomorphic foliations by curves are discussed.
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References
ARNOLD, V.: Chapïtres supplementaires de la théorie des équations differentielles ordinaires, editions MIR, Moscou 1980.
DOUADY, A.: Le problème des modules pour les variétés analytiques complexes (d’après M. Kuranishi), Seminaire Bourbaki, Exposé 277, 1964/65.
DOUADY, A.: ‘Le problème des modules pour les sous-spaces analytiques compacts d’un espace analytique donné’, Ann. Inst. Fourier 16 (1966), 1–95.
DUCHAMP, T. and M. KALKA: ‘Deformation theory of holomorphic foliations’, J. Diff. Geom. 14 (1979), 317–337.
GIRBAU, J., A. HAEFLIGER, and D. SUNDARARAMAN: ‘On deformations of transversely holomorphic foliations’, Journal für die Reine und Angewandte Mathematik 345 (1983), 122–147.
GOMEZ-MONT, X.: ‘Universal families of foliations by curves’, in Proc. Conf. Dyn. Syst. Dijon 1985, ed. by D. Cerveau, R. Moussu, to appear.
GOMEZ-MONT, X.: ‘The tranverse dynamics of a holomorphic flow’, publicación preliminar, Inst. Mat. U.N.A.M. 109 (1986).
KODAIRA, K. and D.C. SPENCER: ‘Multifoliate structures’, Ann. Math. 74 (1961), 52–100.
KURANISHI, M.: ‘On the locally complete families of complex analytic structures’, Ann. of Math. 75 (1962), 536–577.
POURCIN, G.: ‘Théorème de Douady au dessus de S. Ann. Scuola Norm. Sup. di Pisa 23 (1969), 451–459.
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© 1989 Kluwer Academic Publishers
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Mont, X.G., Sundararaman, D. (1989). Remarks on the Versal Families of Deformations of Holomorphic and Transversely Holomorphic Foliations. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2643-1_19
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DOI: https://doi.org/10.1007/978-94-009-2643-1_19
Publisher Name: Springer, Dordrecht
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