Corrigendum: On subadditivity of the logarithmic Kodaira dimension

TL;DR

This paper discusses the failure of certain inequalities related to the logarithmic Kodaira dimension and proposes weaker, still useful inequalities to address this issue.

Contribution

It identifies gaps in previous proofs of subadditivity inequalities and introduces alternative inequalities that remain valid for applications.

Findings

Counterexample showing $ppa_\sigma e ppa_ u$

Weaker inequalities still hold and are sufficient for applications

Clarifies limitations of previous proofs in the literature

Abstract

John Lesieutre constructed an example satisfying $\kappa_\sigma\ne \kappa_\nu$. This says that the proof of the inequalities in Theorems 1.3, 1.9, and Remark 3.8 in [O. Fujino, On subadditivity of the logarithmic Kodaira dimension, J. Math. Soc. Japan 69 (2017), no. 4, 1565--1581] is insufficient. We claim that some weaker inequalities still hold true and they are sufficient for various applications.