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Foliations with positive slopes and birational stability of orbifold cotangent bundles
Publications Mathématiques de l'IHÉS, Volume 129 (2019), pp. 1-49
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Let X be a smooth connected projective manifold, together with an snc orbifold divisor Δ, such that the pair (X,Δ) is log-canonical. If K X +Δ is pseudo-effective, we show, among other things, that any quotient of its orbifold cotangent bundle has a pseudo-effective determinant. This improves considerably our previous result (Campana and Păun in Ann. Inst. Fourier. 65:835, 2015), where generic positivity instead of pseudo-effectivity was obtained. One of the new ingredients in the proof is a version of the Bogomolov-McQuillan algebraicity criterion for holomorphic foliations whose minimal slope with respect to a movable class (instead of an ample complete intersection class) is positive.

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DOI: 10.1007/s10240-019-00105-w

Frédéric Campana 1; Mihai Păun 1

1 
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     title = {Foliations with positive slopes and birational stability of orbifold cotangent bundles},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {1--49},
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Frédéric Campana; Mihai Păun. Foliations with positive slopes and birational stability of orbifold cotangent bundles. Publications Mathématiques de l'IHÉS, Volume 129 (2019), pp. 1-49. doi: 10.1007/s10240-019-00105-w

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