An effective version of a theorem of Kawamata on the Albanese map

TL;DR

This paper extends Kawamata's theorem to better understand when the Albanese map is surjective or an algebraic fiber space, advancing the birational analysis of complex varieties.

Contribution

It generalizes Kawamata's theorem to establish criteria for the Albanese map's surjectivity and fiber space structure.

Findings

Criteria for Albanese map being surjective

Conditions for Albanese map to be an algebraic fiber space

Enhanced understanding of birational properties of complex varieties

Abstract

This paper is devoted to study the birational properties of the Albanese map. I generalize a theorem of Kawamata to tell when the Albanese map is surjective and when it is an algebraic fiber space.