Note on Iitaka Conjecture $C_{n,m}$

Abstract

Let \( f: X \to Y \) be an algebraic fiber space, where \( X \) and \( Y \) are smooth projective varieties of dimensions \( n \) and \( m \), respectively. In \cite{Caopaun}, Cao and P\u{a}un proved \( C_{n,m} \) when \( Y \) has maximal Albanese dimension. In this paper, we prove \( C_{n,m} \) in the case where the Albanese dimension $\alpha(Y)$ of \( Y \) satisfies \( \alpha(Y) \geq m-2 \).