English

On Junyan Cao's vanishing theorem for pseudoeffective line bundles

Algebraic Geometry 2020-11-30 v1 Complex Variables

Abstract

Junyan Cao has obtained a very general vanishing theorem, valid on any compact K\"ahler manifold, for the cohomology groups with values in a pseudoeffective line bundle twisted by the associated multiplier ideal sheaf. In this note, we give a version of this result in terms of the numerical dimension of the line bundle, instead of the numerical dimension of a given singular metric, which can be smaller.

Keywords

Cite

@article{arxiv.2011.13673,
  title  = {On Junyan Cao's vanishing theorem for pseudoeffective line bundles},
  author = {Xiaojun Wu},
  journal= {arXiv preprint arXiv:2011.13673},
  year   = {2020}
}

Comments

8 pages

R2 v1 2026-06-23T20:32:58.109Z