On the restriction of the moduli part to a reduced divisor

Abstract

Let $f:(X,\Delta )\to Y$ be a fibration such that $K_X+\Delta$ is torsion along the fibres of $f$. Assume that $Y$ has dimension 2, or that $Y$ has dimension 3 and the fibres have dimension at most 3. Then the restriction of the moduli part to its augmented base locus is semiample.

arXiv comment52 pages, comments are welcome