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arXiv · 1308.2033

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

Shin-ichi Matsumura
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Abstract

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 dbar-equation by using the de Rham-Weil isomorphism between the dbar-cohomology and the check{C}ech cohomology.

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Shin-ichi Matsumura. 2013-08-09. An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities. https://arxiv.org/abs/1308.2033

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