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On algebraic fiber spaces over varieties of maximal Albanese dimension

Jungkai A. Chen·Christopher D. Hacon
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Abstract

We study algebraic fiber spaces $f:X \longrightarrow Y$ where $Y$ is of maximal Albanese dimension. In particular we give an effective version a theorem of Kawamata: If $P_m(X)=1$ for some $m \ge 2$, then the Albanese map of $X$ is surjective. Combining this with \cite{CH} it follows that $X$ is birational to an abelian variety if and only if $P_2(X)=1$ and $q(X)= \text{\rm dim} (X)$.

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Jungkai A. Chen, Christopher D. Hacon. 2000-11-07. On algebraic fiber spaces over varieties of maximal Albanese dimension. https://arxiv.org/abs/math/0011042

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