On Ahlfors currents

We answer a basic question in Nevanlinna theory that Ahlfors currents associated to the same entire curve may be nonunique. Indeed, we will construct one exotic entire curve which produces infinitely many cohomologically different Ahlfors currents. Moreover, concerning Siu's decomposition, for an arbitrary positive integer k or k=infinity, some of the obtained Ahlfors currents have singular parts supported on k irreducible curves. In addition, they can have nonzero diffuse parts as well, which answers a question of Brunella. This is joint work with Dinh Tuan Huynh.