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Note on Iitaka Conjecture $C_{n,m}$
Houari Benammar Ammar
https://arxiv.org/abs/2510.06412 https://arxiv.org/pdf/2510.06412

Note on Iitaka Conjecture $C_{n,m}$
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 Păun proved \( C_{n,m} \) when \( Y \) has maximal Albanese dimension. In this short note, we prove \( C_{n,m} \) in the cases where the Albanese dimension $α(Y)$ of \( Y \) satisfies \( α(Y) = m-1 \) or \( α(Y) = m-2 \).