English

Log Calabi-Yau fibrations

Algebraic Geometry 2018-11-29 v2

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)(X,B) with good singularities and a projective morphism XZX\to Z such that KX+BK_X+B is numerically trivial over ZZ. 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.

Keywords

Cite

@article{arxiv.1811.10709,
  title  = {Log Calabi-Yau fibrations},
  author = {Caucher Birkar},
  journal= {arXiv preprint arXiv:1811.10709},
  year   = {2018}
}

Comments

Version 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

R2 v1 2026-06-23T06:21:14.102Z