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.KeywordsOpen SubsetCompact ManifoldAnalytic SpaceGeneric RankCoherent SheafThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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