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BIBTEX RIS

Complex Codimension One Singular Foliations and Godbillon–Vey Sequences

2007; Independent University of Moscow; Volume: 7; Issue: 1 Linguagem: Inglês

10.17323/1609-4514-2007-7-1-21-54

ISSN

1609-4514

Autores

Dominique Cerveau, Alcides Lins Neto, Frank Loray, Jorge Vitório Pereira, Frédéric Touzet,

Tópico(s)

Algebraic Geometry and Number Theory

Resumo

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.

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