Foliations with positive slopes and birational stability of orbifold cotangent bundles

Campana, Frédéric; Păun, Mihai

doi:10.1007/s10240-019-00105-w

Article

Foliations with positive slopes and birational stability of orbifold cotangent bundles

Campana, Frédéric ¹ ; Păun, Mihai ¹

¹

Publications Mathématiques de l'IHÉS, Tome 129 (2019), pp. 1-49

Résumé

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.

MR Zbl

DOI : 10.1007/s10240-019-00105-w

Affiliations des auteurs :

Campana, Frédéric ¹ ; Păun, Mihai 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},
     year = {2019},
     publisher = {Springer Berlin Heidelberg},
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     volume = {129},
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     zbl = {1423.14109},
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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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