Date(s) - 10/01/2017
11 h 00 min - 12 h 00 min
In this talk, we will explain some strategy towards the Green-Griffiths-Lang conjecture for surfaces of general type, pursuing McQuillan’s philosophy and the recent discovery “strongly of general type” by Jean-Pierre Demailly. We mainly deal with the algebraic degeneracy of entire curves tangent to holomorphic foliations by curves. We introduce the definition of weakly reduced singularities for foliations by curves, which is less demanding than the “reduced singularities”, and study the intersection of Ahlfors current with the normal bundles of such foliations. We also explain our extension of McQuillan’s “Diophantine approximation” for foliations to higher dimensional manifolds.