On Effective log Iitaka Fibration for 3-folds and 4-folds

TL;DR

This paper proves the effectiveness of the log Iitaka fibration for certain low-dimensional varieties, completing the proof in dimension two and establishing bounds on the moduli part when fibers are of dimension two.

Contribution

It establishes the effectiveness of the log Iitaka fibration for varieties up to dimension four and completes the proof in dimension two, also bounding the moduli part for specific fibers.

Findings

Proves effectiveness of log Iitaka fibration in dimension ≤4.

Completes proof of effectiveness in dimension two.

Bounds the denominator of the moduli part for fibers of dimension two.

Abstract

We prove the effectiveness of the log Iitaka fibration in Kodaira codimension two for varieties of dimension$\le 4$. In particular, we finish the proof of effective log Iitaka fibration in dimension two. Also, we show that for the log Iitaka fibration, if the fiber is of dimension two, the denominator of the moduli part is bounded.