Cotangent bundle

Trigonometric functions

Engineering

Aerospace engineering

Pure mathematics

Stability (learning theory)

Computer science

Divisor (algebraic geometry)

Mathematics

Holomorphic function

Mathematical analysis

Orbifold

Artificial intelligence

Geometry

Intersection (aeronautics)

Quotient

Class (philosophy)

Machine learning

Publications mathématiques de l IHÉS

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.

Foliations with positive slopes and birational stability of orbifold cotangent bundles