A footnote to a theorem of Kawamata

TL;DR

This paper proves that under certain conditions, the quasi-Albanese map of a quasi-projective variety is proper in codimension 1, confirming a conjecture by Iitaka and building on Kawamata's earlier work.

Contribution

It establishes the properness of the quasi-Albanese map in codimension 1 under specific geometric conditions, extending Kawamata's theorem.

Findings

The quasi-Albanese map is proper in codimension 1 under the given hypotheses.

Confirms Iitaka's conjecture regarding the properness of the quasi-Albanese map.

Builds on Kawamata's theorem about the birationality of the quasi-Albanese map.

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.