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15 January 2002 On algebraic fiber spaces over varieties of maximal Albanese dimension
Jungkai A. Chen, Christopher D. Hacon
Duke Math. J. 111(1): 159-175 (15 January 2002). DOI: 10.1215/S0012-7094-02-11115-6

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 $q(X)=\dim(X)$.

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Jungkai A. Chen. Christopher D. Hacon. "On algebraic fiber spaces over varieties of maximal Albanese dimension." Duke Math. J. 111 (1) 159 - 175, 15 January 2002. https://doi.org/10.1215/S0012-7094-02-11115-6

Information

Published: 15 January 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1055.14010
MathSciNet: MR1876444
Digital Object Identifier: 10.1215/S0012-7094-02-11115-6

Subjects:
Primary: 14D06
Secondary: 14J10

Rights: Copyright © 2002 Duke University Press

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Vol.111 • No. 1 • 15 January 2002
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