We show that any fibration of a special compact K{a}hler manifold X onto an Abelian variety has no multiple fibre in codimension one. This statement strengthens and extends previous results of Kawamata and Viehweg when $kappa$(X) = 0. This also corrects the proof given in [2], 5.3 which was incomplete.
We give a simplified proof (in characteristic zero) of the decomposition theorem for complex projective varieties with klt singularities and numerically trivial canonical bundle. The proof rests in an essential way on most of the partial results of the previous proof obtained by many authors, but avoids those in positive characteristic by S. Druel. The single to some extent new contribution is an algebraicity and bimeromorphic splitting result for generically locally trivial fibrations with fibres without holomorphic vector fields. We give first the proof in the easier smooth case, following the same steps as in the general case, treated next.
