Pluricanonical maps of varieties of Albanese fiber dimension two

TL;DR

This paper proves that for smooth projective varieties of Albanese fiber dimension two and of general type, the 6-canonical map is birational, with some results also for the 5-canonical map under additional conditions.

Contribution

It establishes birationality of the 6-canonical map for these varieties and provides conditions under which the 5-canonical map is also birational.

Findings

6-canonical map is birational for these varieties

5-canonical map is birational under certain geometric restrictions

Advances understanding of pluricanonical maps in algebraic geometry

Abstract

In this paper we prove that for any smooth projective variety of Albanese fiber dimension two and of general type, the 6-canonical map is birational. And we also show that the 5-canonical map is birational for any such variety with some geometric restrictions.