Abstract:

We obtain a Le Potier-type isomorphism theorem which relates holomorphic vector bundles with multiplier submodule sheaves associated to strongly Nakano semi-positive singular hermitian metrics to the tautological line bundles with multiplier ideal sheaves. As applications, we obtain a Kollar-type infectivity theorem, a Nadel-type vanishing theorem and a singular holomorphic Morse inequalities for holomorphic vector bundles. This is the joint work with Zhuo Liu, Hui Yang and Xiangyu Zhou.