We will introduce foliations and related notions (see [1, §3]). We will also introduce various notions of slopes and discuss their properties [2, Prop 2.4]. We will explain how conditions on slopes lead to some vanishing results [2, Lem 2.5] and discuss properties of slopes and foliations under birational modifications [2, Lem 2.12, Rem 3.3]. Finally we will explain and outline the main steps of the proofs of statements of in [2, §4].

 

Ref. 

[1] Stéphane Druel. A decomposition theorem for singular spaces with trivial canonical class of dimension at most five. Invent. Math., 211(1):245–296, 2018. 

[2] Frédéric Campana and Mihai Paun, Foliations with positive slopes and birational stability of orbifold cotangent bundles. Publ. Math. Inst. Hautes Études Sci., 129:1–49, 2019.