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On the characterization of abelian varieties for log pairs in zero and positive characteristic

Yuan Wang

Algebraic Geometry mathscidoc:1910.43623

arXiv preprint arXiv:1610.05630, 2016.10
Let (X, ) be a pair. We study how the condition (X, ) causes surjectivity or birationality of the Albanese map and the Albanese morphism of (X, ) in both characteristic (X, ) and characteristic (X, ) . In particular in characteristic (X, ) we generalize Kawamata's result to the cases of log canonial pairs, and in characteristic (X, ) we generalize a result of Hacon-Patakfalvi to the cases of log pairs. Moreover we show that if (X, ) is a normal projective threefold in characteristic (X, ) , the coefficients of the components of (X, ) are (X, ) and (X, ) is semiample, then the Albanese morphism of (X, ) is surjective under reasonable assumptions on (X, ) and the singularities of the general fibers of the Albanese morphism. This is a positive characteristic analog in dimension 3 of a result of Zhang on a conjecture of Demailly-Peternell-Schneider.
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@inproceedings{yuan2016on,
  title={On the characterization of abelian varieties for log pairs in zero and positive characteristic},
  author={Yuan Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020204528953796152},
  booktitle={arXiv preprint arXiv:1610.05630},
  year={2016},
}
Yuan Wang. On the characterization of abelian varieties for log pairs in zero and positive characteristic. 2016. In arXiv preprint arXiv:1610.05630. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020204528953796152.
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