On Junyan Cao's vanishing theorem for pseudoeffective line bundles

英文摘要：

Junyan Cao has obtained a very general vanishing theorem, valid on any compact Kähler 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.