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Pré-Publication, Document De Travail Année : 2011

Singular foliations with trivial canonical class

Résumé

This paper is devoted to describe the structure of singular codimension one foliations with numerically trivial canonical bundle on projective manifolds. To achieve this goal we study the reduction modulo p of foliations, describe the structure of first integrals of (semi-)stable foliations with (negative) zero canonical bundle, establish a criterium for uniruledness of projective manifolds, and investigate the deformation of free morphisms along foliations. This paper also contains a classification of the irreducible components of the space of foliations with KF ≤ 0 on Fano 3-folds with rank one Picard group, and new information about the structure of codimension one foliations on P^n of degree smaller than or equal to 2n − 3.
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Dates et versions

hal-00607116 , version 1 (07-07-2011)
hal-00607116 , version 2 (22-12-2017)
hal-00607116 , version 3 (29-08-2018)

Identifiants

  • HAL Id : hal-00607116 , version 1

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Frank Loray, Jorge Vitorio Pereira, Frédéric Touzet. Singular foliations with trivial canonical class. 2011. ⟨hal-00607116v1⟩
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