A criterion for associated bundles and the weak Beauville--Bogomolov decomposition

Abstract

We give a criterion for a fibration to be an associated fibre bundle. As an application, we show that, under suitable singularity and Cartier-index assumptions, any surjective fibration $X\to Y$ with nef $-K_{X/Y}$ is an associated fibre bundle. From this, we also deduce a weak Beauville--Bogomolov decomposition for varieties with nef anticanonical divisor.

23 pages. Comments welcome!