On birational boundedness of Fano fibrations

Chen Jiang Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-Ku, Tokyo 153-8914, Japan

Algebraic Geometry mathscidoc:2203.45007

American Journal of Mathematics, 140, (5), 1253-1276, 2018.10
We investigate birational boundedness of Fano varieties and Fano fibrations. We establish an inductive step towards birational boundedness of Fano fibrations via conjectures related to bound- edness of Fano varieties and Fano fibrations. As corollaries, we provide approaches towards birational boundedness and boundedness of anti-canonical volumes of varieties of ε-Fano type. Furthermore, we show birational boundedness of 3-folds of ε-Fano type.
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  title={On birational boundedness of Fano fibrations},
  author={Chen Jiang},
  booktitle={American Journal of Mathematics},
Chen Jiang. On birational boundedness of Fano fibrations. 2018. Vol. 140. In American Journal of Mathematics. pp.1253-1276. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220316111108395857978.
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