Foliations with positive slopes and birational stability of orbifold cotangent bundles

TL;DR

This paper investigates the positivity properties of orbifold cotangent bundles in log canonical pairs, establishing pseudo-effectiveness of determinants for their quotients and generalizing algebraicity criteria for foliations.

Contribution

It introduces a new generalization of the Bogomolov-McQuillan algebraicity criterion applicable to holomorphic foliations with positive minimal slope.

Findings

Quotients of orbifold cotangent bundles have pseudo-effective determinants.

Generalization of algebraicity criterion for foliations with positive slope.

Results apply to log-smooth log canonical pairs with pseudo-effective canonical bundles.

Abstract

In this article we consider log canonical pairs which are log-smooth. If the corresponding canonical bundle is pseudo-effective, then we show that any quotient of the orbifold cotangent bundle of the pair has a pseudo-effective determinant. One of the new ingredients in the proof is a generalization of the Bogomolov-McQuillan algebraicity criterion in the context of holomorphic foliations whose minimal slope with respect to a movable class is positive.