Geodesic
Article
Foliations with positive slopes and birational stability of orbifold cotangent bundles
Publications Mathématiques de l'IHÉS, Tome 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.

DOI : 10.1007/s10240-019-00105-w

Campana, Frédéric 1 ; Păun, Mihai 1

1 
@article{PMIHES_2019__129__1_0,
     author = {Campana, Fr\'ed\'eric and P\u{a}un, Mihai},
     title = {Foliations with positive slopes and birational stability of orbifold cotangent bundles},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {1--49},
     publisher = {Springer Berlin Heidelberg},
     address = {Berlin/Heidelberg},
     volume = {129},
     year = {2019},
     doi = {10.1007/s10240-019-00105-w},
     mrnumber = {3949026},
     zbl = {1423.14109},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00105-w/}
}
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Campana, Frédéric; Păun, Mihai. Foliations with positive slopes and birational stability of orbifold cotangent bundles. Publications Mathématiques de l'IHÉS, Tome 129 (2019), pp. 1-49. doi: 10.1007/s10240-019-00105-w

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