On algebraic fiber spaces over varieties of maximal Albanese dimension
Jungkai A. Chen and Christopher D. Hacon
Source: Duke Math. J. Volume 111, Number 1 (2002), 159-175.
Abstract
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 $q(X)=\dim(X)$.
Primary Subjects: 14D06
Secondary Subjects: 14J10
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1087575010
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MR1876444
Digital Object Identifier: doi:10.1215/S0012-7094-02-11115-6
Zentralblatt MATH identifier:
01820869
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