On algebraic fiber spaces over varieties of maximal Albanese dimension
Chen, Jungkai A. ; Hacon, Christopher D.
Duke Math. J., Tome 115 (2002) no. 1, p. 159-175 / Harvested from Project Euclid
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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 $q(X)=\dim(X)$.
Publié le : 2002-01-15
Classification:  14D06,  14J10 
@article{1087575010,
     author = {Chen, Jungkai A. and Hacon, Christopher D.},
     title = {On algebraic fiber spaces over varieties of maximal Albanese dimension},
     journal = {Duke Math. J.},
     volume = {115},
     number = {1},
     year = {2002},
     pages = { 159-175},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087575010}
}

Chen, Jungkai A.; Hacon, Christopher D. On algebraic fiber spaces over varieties of maximal Albanese dimension. Duke Math. J., Tome 115 (2002) no. 1, pp.  159-175. http://gdmltest.u-ga.fr/item/1087575010/