Remarks on algebraic fiber spaces

TL;DR

This paper discusses properties of algebraic fiber spaces, generalizes a key theorem related to Albanese dimension, and proves an inequality of irregularities, extending existing results in algebraic geometry.

Contribution

It provides a generalization of a main theorem on Albanese dimension and includes a new inequality of irregularities for algebraic fiber spaces.

Findings

Generalization of the main theorem of [F2] on Albanese dimension

Proved an inequality of irregularities for algebraic fiber spaces

Exposition of Fujita-Kawamata's semi-positivity theorem

Abstract

In this paper, we collect basic properties of the Albanese dimension and explain how to generalize the main theorem of [F2](math.AG/0204262). This paper is a supplement and a generalization of [F2]. We also prove an inequality of irregularities for algebraic fiber spaces in the appendix, which is an exposition of Fujita-Kawamata's semi-positivity theorem.