Duke Mathematical Journal

On algebraic fiber spaces over varieties of maximal Albanese dimension

Jungkai A. Chen and Christopher D. Hacon

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

Article information

Duke Math. J., Volume 111, Number 1 (2002), 159-175.

First available in Project Euclid: 18 June 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14D06: Fibrations, degenerations
Secondary: 14J10: Families, moduli, classification: algebraic theory


Chen, Jungkai A.; Hacon, Christopher D. On algebraic fiber spaces over varieties of maximal Albanese dimension. Duke Math. J. 111 (2002), no. 1, 159--175. doi:10.1215/S0012-7094-02-11115-6. https://projecteuclid.org/euclid.dmj/1087575010

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