Resumen de Algebraic Reduction Theorem for complex codimension one singular foliations

Dominique Cerveau , Alcides Lins-Neto, Frank Loray , J.V. Pereira, Frédéric Touzel

• Let $M$ be a compact complex manifold equipped with $n=\dim(M)$ meromorphic vector fields that are linearly independent at a generic point. The main theorem is the following. If $M$ is not bimeromorphic to an algebraic manifold, then any codimension one complex foliation $\mathcal F$ with a codimension $\ge2$ singular set is the meromorphic pull-back of an algebraic foliation on a lower dimensional algebraic manifold, or $\mathcal F$ is transversely projective outside a proper analytic subset. The two ingredients of the proof are the Algebraic Reduction Theorem for the complex manifold $M$ and an algebraic version of Lie's first theorem which is due to J. Tits