Singular hermitian metrics on vector bundles

We introduce a notion of singular hermitian metrics (s.h.m.) for holomorphic vector bundles and de ne positivity in view of L2-estimates. Associated with a suitably positive s.h.m. there is a (coherent) sheaf 0-th kernel of a certain d FF-complex. We prove a vanishing theorem for the cohomology of this sheaf. All this generalizes to the case of higher rank… CONTINUE READING