Numerical dimension and a Kawamata-Viehweg-Nadel type vanishing theorem on compact K\'ahler manifolds
- Resource Type
- Working Paper
- Authors
- Cao, Junyan
- Source
- Compositio Math. 150 (2014) 1869-1902
- Subject
- Mathematics - Algebraic Geometry
- Language
Let $X$ be a compact K\"ahler manifold and let $(L, \varphi)$ be a pseudo-effective line bundle on $X$. We first define a notion of numerical dimension of pseudo-effective line bundles with singular metrics, and then discuss the properties of this type numerical dimension. We finally prove a very general Kawamata-Viehweg-Nadel type vanishing theorem on an arbitrary compact K\"ahler manifold.