Kodaira dimension of fibrations over abelian varieties

TL;DR

This paper establishes new additivity and subadditivity results for the log Kodaira dimension in algebraic fiber spaces over abelian varieties and varieties of maximal Albanese dimension, advancing understanding in algebraic geometry.

Contribution

It introduces novel additivity and subadditivity theorems for log Kodaira dimension in fiber spaces over abelian and maximal Albanese dimension varieties.

Findings

Proved additivity of log Kodaira dimension over abelian varieties.

Established superadditivity for fiber spaces over maximal Albanese dimension.

Demonstrated subadditivity for log pairs.

Abstract

We prove an additivity result for the log Kodaira dimension of algebraic fiber spaces over abelian varieties, a superadditivity result for fiber spaces over varieties of maximal Albanese dimension, as well as a subadditivity result for log pairs.