Complex codimension one singular foliations and Godbillon-Vey sequences

By D. Cerveau, A. L. Neto, Frank Loray, J. Pereira, Fr'ed'eric Touzet. 2004

55 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/dd681b3a5c89d68d28a7e4ca579d2dcd02a95787

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In Applied Mathematics

1. Frank Loray
2. J. Pereira
3. Fr'ed'eric Touzet
4. S. Druel

In Geometry and Topology

1. Frank Loray
2. J. Pereira
3. Fr'ed'eric Touzet
4. S. Druel

Citations in the corpus

• Singular foliations with trivial canonical class (2011, methodology): “In 1997, one year after the publication of Cerveau-Lins Neto paper, appeared a paper [50] by Polishchuk which, among other things, contains a classification of Poisson structures on P3 under restrictive hypothesis on their singular set.”