On algebraic fiber spaces over varieties of maximal Albanese dimension

Details On algebraic fiber spaces over varieties of maximal Albanese dimension On algebraic fiber spaces over varieties of maximal Albanese dimension

2000-11-07

arxiv.org/abs/math/0011042v1

Mathematics

Algebraic Geometry

Scientific paper

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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