Abstract:
Let $\mathscr{F}$ be a codimension one holomorphic foliation on a smooth projective manifold $X$. We can associate to $\mathscr{F}$ its canonical line bundle (analogue of the canonical line bundle of a manifold) and its conormal line bundle. I will discuss positivity properties of these line bundles; also I will use positivity to prove some classification results for foliations.