Mathematics

The existence of sufficiently positive subsheaves  of the tangent bundle of a complex projective manifold Ximposes strong restrictions on X.In particular, several special varieties can be characterized by positivity properties of their tangent bundle.There are various notions of positivity for distributions on complex projective manifolds.In this talk we consider distributions having big slope with respect to curve classes,obtaining characterizations of generic projective space bundles  in terms of  movable curve classes.We then apply this result to investigate algebraicity of leaves of foliations, providinga lower bound for the algebraic rank of a foliation in terms of invariants measuring positivity.This is a joint work with Stéphane Druel.