A Kollár-type vanishing theorem

Abstract

Let $f:X\to Y$ be a smooth fibration between two complex manifolds $X$ and $Y$, and let $L$ be a pseudo-effective line bundle on $X$. We obtain a sufficient condition for $R^q{f}_{\ast }(K_{X/Y}\otimes L)$ to be reflexive and hence derive a Kollár-type vanishing theorem.

11 pages, accepted for publication in Mathematische Zeitschrift; added references for Introduction