Threefolds of Kodaira dimension one

TL;DR

This paper proves that for smooth complex projective threefolds with Kodaira dimension one, the pluricanonical map becomes birational to the Iitaka fibration for sufficiently large divisible m, specifically m ≥ 5868.

Contribution

It establishes an explicit bound on m ensuring the pluricanonical map's birationality to the Iitaka fibration for threefolds of Kodaira dimension one.

Findings

Pluricanonical map is birational to the Iitaka fibration for m ≥ 5868 divisible by 12.

Provides an explicit bound improving understanding of pluricanonical maps.

Advances classification theory of algebraic threefolds.

Abstract

We prove that for any smooth complex projective threefold of Kodaira dimension one, the $m$-th pluricanonical map is birational to the Iitaka fibration for every $m\geq5868$ and divisible by $12$.