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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
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.
Received: 15.05.2020 and 14.10.2020
Citation:
C. Birkar, Y. Chen, “Singularities on toric fibrations”, Mat. Sb., 212:3 (2021), 20–38; Sb. Math., 212:3 (2021), 288–304
Linking options:
https://www.mathnet.ru/eng/sm9446https://doi.org/10.1070/SM9446 https://www.mathnet.ru/eng/sm/v212/i3/p20
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Abstract page: | 324 | Russian version PDF: | 49 | English version PDF: | 22 | Russian version HTML: | 100 | References: | 51 | First page: | 12 |
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