A footnote to a theorem of Kawamata

Abstract

Kawamata has shown that the quasi-Albanese map of a quasi-projective variety with log-irregularity equal to the dimension and log-Kodaira dimension 0 is birational. In this note we show that under these hypotheses the quasi-Albanese map is proper in codimension 1 as conjectured by Iitaka.

Added an addendum by O. Fujino, M. Mendes Lopes, R. Pardini and S. Tirabassi that contains an alternative proof of Theorem A in the paper and explains how to avoid an unsubstantiated claim made in the original proof