Complex codimension one singular foliations and Godbillon-Vey sequences

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dc.creatorCerveau, Dominique
dc.creatorNeto, Alcides Lins
dc.creatorLoray, Frank
dc.creatorPereira, Jorge Vitorio
dc.creatorTouzet, Frederic
dc.date2004-06-15
dc.date2005-12-09
dc.date.accessioned2026-07-07T09:58:17Z
dc.date.available2026-07-07T09:58:17Z
dc.descriptionLet F be a codimension one singular holomorphic foliation on a compact complex manifold M. Assume that there exists a meromorphic vector field X on M generically transversal to F. Then, we prove that F is the meromorphic pull-back of an algebraic foliation on an algebraic manifold N, or F is transversely projective outside a compact hypersurface, improving our previous work (see version 1). Such a vector field insures the existence of a global meromorphic Godbillon-Vey sequence for the foliation F. We derive sufficient conditions on this sequence insuring such alternative. For instance, if there exists a finite Godbillon-Vey sequence or if the Godbillon-Vey invariant is zero, then either F is the pull-back of a foliation on a surface, or F is transversely projective. We illustrate these results with many examples.
dc.descriptionA part of version 1 will appear in Comment. Math. Helv. 81 (2006), namely the main theorem which actually did not need use of Godbillon-Vey sequences ; this was observed by E. Ghys. In this new version, we weaken assumptions for the main theorem and really use Godbillon-Vey sequences to prove it. Auxiliary results are left unchanged
dc.identifierhttps://arxiv.org/abs/math/0406293
dc.identifierhttp://arxiv.org/abs/math/0406293
dc.identifierMoscow mathematical journal 7 (2007) 21-54
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167664
dc.subjectClassical Analysis and ODEs
dc.subjectDifferential Geometry
dc.subject37F75; 34Mxx
dc.titleComplex codimension one singular foliations and Godbillon-Vey sequences
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