An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities

The purpose of this paper is to establish an injectivity theorem generalized to pseudo-effective line bundles with transcendental (non-Algebraic) singular hermitian metrics and multiplier ideal sheaves. As an application, we obtain a Nadel type vanishing theorem. For the proof, we study the asymptotic behavior of the harmonic forms with respect to a family of regularized metrics, and give a method to obtain L²-estimates of solutions of the ℓ-equation by using the de Rham-Weil isomorphism between the ℓ-cohomology and the Cech cohomology.