SINGULAR HERMITIAN METRICS AND THE DECOMPOSITION THEOREM OF CATANESE, FUJITA, AND KAWAMATA

We prove that a torsion-free sheaf F endowed with a singular hermitian metric with semi-positive curvature and satisfying the minimal extension property admits a direct-sum decomposition F similar or equal to U circle plus A where U is a hermitian flat bundle and A is a generically ample sheaf. The result applies to the case of direct images of relative pluricanonical bundles f & lowast;omega(circle times m)(X/Y) under a surjective morphism f: X -> Y of smooth projective varieties with m >= 2. This extends previous results of Fujita, Catanese--Kawamata, and Iwai.