Luca Rizzi, Local Systems, Algebraic Foliations and Fibrations

Given a semistable fibration f : X → B I will show a correspondence between foliations on X and local systems on B. Building up on this correspondence we will find conditions that give maximal rationally connected fibrations in terms of data on the foliation. We will develop the ideas of the Castelnuovo-de Franchis theorem in the case of p-forms and show when, under some natural conditions, a line subbundle of the sheaf of p-forms induces the Iitaka fibration. Based on a joint work with Prof. Francesco Zucconi.