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Article Dans Une Revue International Mathematics Research Notices Année : 2016

Foliations and Webs Inducing Galois Coverings

Résumé

We introduce the notion of Galois holomorphic foliation on the complex projective space as that of foliations whose Gauss map is a Galois covering when restricted to an appropriate Zariski open subset. First, we establish general criteria assuring that a rational map between projective manifolds of the same dimension defines a Galois covering. Then, these criteria are used to give a geometric characterization of Galois foliations in terms of their inflection divisor and their singularities. We also characterize Galois foliations on P-2 admitting continuous symmetries, obtaining a complete classification of Galois homogeneous foliations.

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Dates et versions

hal-01380564 , version 1 (13-10-2016)

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Andrés Beltrán, Maycol Falla Luza, David Marín, Marcel Nicolau. Foliations and Webs Inducing Galois Coverings. International Mathematics Research Notices, 2016, 2016 (12), pp.3768 - 3827. ⟨10.1093/imrn/rnv249⟩. ⟨hal-01380564⟩
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