$L^2$-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.
Fields of Study & Subjects
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 3 February 2026
- Document type
- Preprint