Iitaka conjecture $C_{n,m}$ in dimension six

TL;DR

This paper proves the Iitaka conjecture $C_{n,m}$ for algebraic fibre spaces in all cases where the total dimension is six or less, advancing understanding in algebraic geometry.

Contribution

The paper establishes the validity of the Iitaka conjecture $C_{n,m}$ for algebraic fibre spaces up to dimension six, filling a significant gap in the conjecture's verification.

Findings

Proves the Iitaka conjecture $C_{n,m}$ for all algebraic fibre spaces with total dimension n ≤ 6.

Extends the known cases of the conjecture to higher dimensions.

Provides new techniques applicable to algebraic geometry in low to moderate dimensions.

Abstract

We prove that the Iitaka conjecture $C_{n,m}$ for algebraic fibre spaces holds up to dimension 6, that is, when $n\le 6$.