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Sbornik: Mathematics, 2021, Volume 212, Issue 3, Pages 351–373
DOI: https://doi.org/10.1070/SM9388 (Mi sm9388) 		 
This article is cited in 1 scientific paper (total in 1 paper)

General elephants for threefold extremal contractions with one-dimensional fibres: exceptional case

S. Moriabc, Yu. G. Prokhorovd

a Kyoto University Institute for Advanced Study, Kyoto University, Kyoto, Japan
b Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan
c Chubu University Academy of Emerging Sciences, Chubu University, Aichi, Japan
d Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
English version PDF (635 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/SM9388
Abstract: Let $(X, C)$ be a germ of a threefold $X$ with terminal singularities along a connected reduced complete curve $C$ with a contraction $f \colon (X, C) \to (Z, o)$ such that $C = f^{-1} (o)_{\mathrm{red}}$ and $-K_X$ is $f$-ample. Assume that each irreducible component of $C$ contains at most one point of index ${>2}$. We prove that a general member $D\in |{-}K_X|$ is a normal surface with Du Val singularities.
Bibliography: 16 titles.
Keywords: terminal singularity, extremal curve germ, flip, divisorial contraction, $\mathbb{Q}$-conic bundle.
Funding agency Grant number
Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University
This work was partially supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.
Received: 25.02.2020 and 27.11.2020
Bibliographic databases:
Document Type: Article
UDC: 512.76
MSC: Primary 14E30; Secondary 14J30, 14J17
Language: English
Original paper language: Russian
Citation: S. Mori, Yu. G. Prokhorov, “General elephants for threefold extremal contractions with one-dimensional fibres: exceptional case”, Sb. Math., 212:3 (2021), 351–373
Citation in format AMSBIB
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\vol 212
\issue 3
\pages 351--373
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    • This publication is cited in the following 1 articles:
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