On multiplicities of fibers of Fano fibrations

TL;DR

This paper links several major conjectures in birational geometry to a new conjecture concerning the multiplicities of fibers in Fano fibrations over curves, aiming to unify and simplify their understanding.

Contribution

It introduces a unifying conjecture on fiber multiplicities that reduces multiple complex conjectures in birational geometry to a single, more manageable problem.

Findings

Reduces Shokurov conjecture to fiber multiplicity conjecture

Connects boundedness of Calabi-Yau varieties to fiber multiplicities

Proposes a new approach to longstanding conjectures in birational geometry

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.