Monodromy of Lagrangian Fibrations

A compact hyperkahler manifold is a higher-dimensional analog of a K3 surface; Lagrangian fibrations of hyperkahler manifolds are higher-dimensional versions of elliptic fibrations of K3 surfaces. A result of Voisin shows that these fibrations yield irreducible real variations of weight one Hodge structures. We show that when the variation is not isotrivial, its underlying local system is irreducible over the complex numbers.