Log Calabi-Yau fibrations

TL;DR

This paper investigates the boundedness and singularity properties of log Calabi-Yau fibrations, especially those with Fano type structures, which are central to various aspects of birational geometry.

Contribution

It provides new insights into the boundedness and singularities of log Calabi-Yau fibrations with Fano type structures, expanding understanding of their geometric properties.

Findings

Boundedness properties of log Calabi-Yau fibrations established

Singularity analysis of fibrations with Fano type structures conducted

Connections to birational geometry components clarified

Abstract

In this paper we study boundedness properties and singularities of log Calabi-Yau fibrations, particularly those admitting Fano type structures. A log Calabi-Yau fibration roughly consists of a pair $(X,B)$ with good singularities and a projective morphism $X\to Z$ such that $K_X+B$ is numerically trivial over $Z$. This class includes many central ingredients of birational geometry such as Calabi-Yau and Fano varieties and also fibre spaces of such varieties, flipping and divisorial contractions, crepant models, germs of singularities, etc.