On the Iitaka fibration of varieties of maximal Albanese dimension

TL;DR

This paper proves that for varieties with maximal Albanese dimension, the tetracanonical map induces the Iitaka fibration, and for those of general type, the tricanonical map is birational, advancing understanding of their canonical maps.

Contribution

It establishes the relationship between canonical maps and the Iitaka fibration for varieties of maximal Albanese dimension, including the birationality of the tricanonical map for varieties of general type.

Findings

Tetracanonical map induces the Iitaka fibration.

Tricanonical map is birational for varieties of general type.

Advances understanding of canonical maps in algebraic geometry.

Abstract

We prove that the tetracanonical map of a variety $X$ of maximal Albanese dimension induces the Iitaka fibration. Moreover, if $X$ is of general type, then the tricanonical map is birational.