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Sbornik: Mathematics, 2021, Volume 212, Issue 3, Pages 288–304
DOI: https://doi.org/10.1070/SM9446
(Mi sm9446)
 

This article is cited in 1 scientific paper (total in 1 paper)

Singularities on toric fibrations

C. Birkara, Y. Chenb

a Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Cambridge University, Cambridge, UK
b Hua Loo-Keng Key Laboratory of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China
References:
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.
Keywords: toric varieties, Shokurov's conjecture, singularities of pairs.
Funding agency Grant number
Royal Society
National Natural Science Foundation of China 11688101
11771426
11621061
The research of C. Birkar was carried out with the support of the Royal Society (UK). The research of Y. Chen was carried out with the support of the National Natural Science Foundation of China (grant nos. 11688101, 11771426 and 11621061).
Received: 15.05.2020 and 14.10.2020
Russian version:
Matematicheskii Sbornik, 2021, Volume 212, Number 3, Pages 20–38
DOI: https://doi.org/10.4213/sm9446
Bibliographic databases:
Document Type: Article
UDC: 512.761
MSC: Primary 14B05, 14M25; Secondary 14E30
Language: English
Original paper language: Russian
Citation: C. Birkar, Y. Chen, “Singularities on toric fibrations”, Mat. Sb., 212:3 (2021), 20–38; Sb. Math., 212:3 (2021), 288–304
Citation in format AMSBIB
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\by C.~Birkar, Y.~Chen
\paper Singularities on toric fibrations
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\pages 20--38
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\jour Sb. Math.
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  • This publication is cited in the following 1 articles:
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    References:51
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