Mathematics – Classical Analysis and ODEs
Scientific paper
2004-06-15
Moscow mathematical journal 7 (2007) 21-54
Mathematics
Classical Analysis and ODEs
A part of version 1 will appear in Comment. Math. Helv. 81 (2006), namely the main theorem which actually did not need use of
Scientific paper
Let 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.
Cerveau Dominique
Loray Frank
Neto Alcides Lins
Pereira Jorge Vitório
Touzet Frederic
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