Numerical dimension and a Kawamata–Viehweg–Nadel-type vanishing theorem on compact Kähler manifolds
By Junyan Cao. Compositio Mathematica, 2012
66 citations recorded by the source corpus.
Abstract Let $X$ be a compact Kähler manifold and let $(L,{\it\varphi})$ be a pseudo-effective line bundle on $X$. We first define a notion of numerical dimension for pseudo-effective line bundles with singular metrics, and then discuss the properties of this numerical dimension. Finally, we prove a very general Kawamata–Viehweg–Nadel-type vanishing theorem on an arbitrary compact Kähler manifold.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/def2a9d4505d7e02faedab6b02bbe2df2cc8e662
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (2013, background): “In his paper [Cao12], Cao proved the former conclusion of the lemma when a quasi-psh function ϕ has analytic singularities.”
- The weighted log canonical threshold (2014, unknown): “We refer to [5], [6], [7], [12], [9], [10], [13] [18], [19], [22], [23], [25], [26] for further information about this number.”