On multiplicities of fibers of Fano fibrations
arXiv:2208.10372
Abstract
In this note, we reduce various conjectures in birational geometry, including Shokurov conjecture on singularities of the base of log Calabi-Yau fibrations of Fano type and boundedness conjecture for rationally connected Calabi-Yau varieties, to a conjecture on multiplicities of fibers of Fano fibrations over curves.
v4=v3: v3 does not appear normally, fixed now. v3: The proof of Lemma 4.7 rewritten to resolve inaccuracy. This note is not intended for publication, since all the conjectures listed in the introduction part have been confirmed. We keep it here for reference