$L^2$-Dolbeault resolutions and Nadel vanishing on weakly pseudoconvex complex spaces with singular Hermitian metrics

Abstract

In this paper, in order to develop a more general $L^2$-theory for the $\overline{\partial }$-operator on complex spaces, we provide $L^2$-Dolbeault fine resolutions and isomorphisms, and $L^2$-estimates, for holomorphic line bundles on complex spaces equipped with singular Hermitian metrics. As applications, we obtain several generalizations of the Nadel vanishing theorem.

arXiv commentv2: 22 pages. Mainly revised the introduction and Section 4 in light of prior work, and removed the former Section 4. v1: 24 pages