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.

## Characterization of generic projective space bundles and applications to foliations

Research Group:

Carolina Araujo

Institution:

IMPA, Rio de Janeiro

Location:

A-139

Schedule:

Thursday, June 14, 2018 - 14:30

Abstract: