On multiplicities of fibers of Fano fibrations

Published 22 Aug 2022 in math.AG | (2208.10372v2)

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.

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