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2 results

A Witt Nadel vanishing theorem for threefolds
Part of
- Surfaces and higher-dimensional varieties
- Birational geometry
Yusuke Nakamura, Hiromu Tanaka
Journal:

Compositio Mathematica / Volume 156 / Issue 3 / March 2020

Published online by Cambridge University Press:

13 January 2020, pp. 435-475

Print publication:

March 2020
- Article
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In this paper, we establish a vanishing theorem of Nadel type for the Witt multiplier ideals on threefolds over perfect fields of characteristic larger than five. As an application, if a projective normal threefold over $\mathbb{F}_{q}$ is not klt and its canonical divisor is anti-ample, then the number of the rational points on the klt-locus is divisible by $q$.

Numerical dimension and a Kawamata–Viehweg–Nadel-type vanishing theorem on compact Kähler manifolds
Part of
- (Co)homology theory
- Holomorphic fiber spaces
Junyan Cao
Journal:

Compositio Mathematica / Volume 150 / Issue 11 / November 2014

Published online by Cambridge University Press:

27 August 2014, pp. 1869-1902

Print publication:

November 2014
- Article
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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.