Kodaira dimension of algebraic fiber spaces over threefolds : Part 1

TL;DR

This paper investigates how the Kodaira dimension behaves in algebraic fiber spaces over threefolds, proving specific cases of the Iitaka Conjecture, especially when the base is a Calabi--Yau threefold.

Contribution

It establishes new cases of the Iitaka Conjecture for fiber spaces over threefolds, including scenarios with Calabi--Yau bases.

Findings

Proved certain cases of the Iitaka Conjecture $C_{n,3}$.

Analyzed the Kodaira dimension behavior over threefold bases.

Included results for fiber spaces with Calabi--Yau threefold bases.

Abstract

We study the behavior of the Kodaira dimension of algebraic fiber spaces over threefolds. We prove some cases of the Iitaka Conjecture $C_{n,3}$, including certain situations where the base variety is a Calabi--Yau threefold.