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 ≃ U 〇 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∗ω_X/Y 〇^m under a surjective morphism f : X → Y of smooth projective varieties with m ≥ 2. This extends previous results of Fujita, Catanese–Kawamata, and Iwai.