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Foliations with positive slopes and birational stability of orbifold cotangent bundles

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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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Authors and Affiliations

  1. Institut Elie Cartan, Université Lorraine, Nancy, France

    Frédéric Campana

  2. KIAS, 85 Hoegiro, Dongdaemun-gu, Seoul, 130-722, South Korea

    Frédéric Campana & Mihai Păun

  3. Institut Universitaire de France, 1, rue Descartes, Paris, 75005, France

    Frédéric Campana

  4. Department of Mathematics, College of Liberal Arts and Sciences, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL, 60607-7045, USA

    Mihai Păun

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  1. Frédéric Campana
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  2. Mihai Păun
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Correspondence to Frédéric Campana.

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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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