Algebraic Reduction Theorem for complex codimension one singular foliations
Dominique Cerveau
Université de Rennes I, FranceAlcides Lins-Neto
Instituto de Matemática Pura e Aplicada, Rio De Janeiro, BrazilFrank Loray
Université Lille I, Villeneuve D'ascq, FranceJorge Vitório Pereira
IMPA, Rio De Janeiro, BrazilFrédéric Touzet
Université de Rennes I, France
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Abstract
Let be a compact complex manifold equipped with meromorphic vector fields that are linearly independent at a generic point. The main theorem is the following. If is not bimeromorphic to an algebraic manifold, then any codimension one complex foliation with a codimension singular set is the meromorphic pull-back of an algebraic foliation on a lower dimensional algebraic manifold, or is transversely projective outside a proper analytic subset. The two ingredients of the proof are the Algebraic Reduction Theorem for the complex manifold and an algebraic version of Lie's first theorem which is due to J. Tits.
Cite this article
Dominique Cerveau, Alcides Lins-Neto, Frank Loray, Jorge Vitório Pereira, Frédéric Touzet, Algebraic Reduction Theorem for complex codimension one singular foliations. Comment. Math. Helv. 81 (2006), no. 1, pp. 157–169
DOI 10.4171/CMH/47