Log Calabi-Yau fibrations

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.

arXiv commentVersion 2: 66 pages, further results are announced at the end of the introduction whose proofs will appear in a sequel joint paper, otherwise the paper is identical to version 1

References in corpus (2)

• The Adjunction Conjecture and its applications
• Birational boundedness of rationally connected Calabi-Yau 3-folds

Cited by in corpus (11)

• Birational boundedness of rationally connected Calabi-Yau 3-folds
• Boundedness of elliptic Calabi-Yau varieties with a rational section
• Shokurov's conjecture on conic bundles with canonical singularities
• Boundedness of the base varieties of certain fibrations
• Existence of flips for generalized lc pairs
• On the boundedness of $n$-folds with $\kappa (X)=n-1$
• Boundedness of $(\epsilon ,n)$-Complements for Surfaces
• Some Results about the Index Conjecture for log Calabi-Yau Pairs
• Sarkisov program for generalized pairs
• Boundedness and volume of generalised pairs
• Rationally connected threefolds with nef and bad anticanonical divisor