Abstract
Let \(X\) be a smooth connected projective manifold, together with an snc orbifold divisor \(\Delta \), such that the pair \((X, \Delta )\) is log-canonical. If \(K_{X}+\Delta \) 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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Campana, F., Păun, M. Foliations with positive slopes and birational stability of orbifold cotangent bundles. Publ.math.IHES 129, 1–49 (2019). https://doi.org/10.1007/s10240-019-00105-w
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DOI: https://doi.org/10.1007/s10240-019-00105-w