Email this article Singularities on toric fibrations
- Authors: Birkar C.1, Chen Y.2
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Affiliations:
- University of Cambridge
- Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences
- Issue: Vol 212, No 3 (2021)
- Pages: 20-38
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/142350
- DOI: https://doi.org/10.4213/sm9446
- ID: 142350
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Abstract
In this paper we investigate singularities on toric fibrations. In this context we study a conjecture of Shokurov (a special case of which is due to M\textsuperscript{c}Kernan) which roughly says that if $(X,B)\to Z$ is an $\varepsilon$-lc Fano-type log Calabi-Yau fibration, then the singularities of the log base $(Z,B_Z+M_Z)$ are bounded in terms of $\varepsilon$ and $\dim X$ where $B_Z$ and $M_Z$ are the discriminant and moduli divisors of the canonical bundle formula. A corollary of our main result says that if $X\to Z$ is a toric Fano fibration with $X$ being $\varepsilon$-lc, then the multiplicities of the fibres over codimension one points are bounded depending only on $\varepsilon$ and $\dim X$. Bibliography: 20 titles.
About the authors
Caucher Birkar
University of Cambridge
Email: c.birkar@dpmms.cam.ac.uk
Yifei Chen
Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of SciencesPhD
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