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Izvestiya: Mathematics, 2016, Volume 80, Issue 5, Pages 884–909
DOI: https://doi.org/10.1070/IM8516 (Mi im8516) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Threefold extremal contractions of type (IIA). I

S. Moriab, Yu. G. Prokhorovcde

a Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan
b Kyoto University Institute for Advanced Study, Kyoto University, Kyoto, Japan
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
d Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
e National Research University "Higher School of Economics" (HSE), Moscow
English version PDF (754 kB) Citations (3) Russian version article
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DOI: https://doi.org/10.1070/IM8516
Abstract: Let $(X,C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible 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 ample. Assume that $(X,C)$ contains a point of type $(\mathrm{IIA})$ and that a general member $H\in|\mathscr O_X|$ containing $C$ is normal. We classify such germs in terms of $H$.
Keywords: extremal contraction, threefold, extremal curve germ, terminal singularity, sheaf.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-02164а
15-01-02158а
15-51-50045Яф_а
Japan Society for the Promotion of Science (A) 25287005
(S) 24224001
The first author's work was partially supported by JSPS KAKENHI Grant Numbers (A) 25287005 and (S) 24224001. The second author's work was partially supported by the RFFI grants 15-01-02164a, 15-01-02158a, 15-51-50045ЯФ$\_$а, and by a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program.
Received: 28.01.2016
Bibliographic databases:
Document Type: Article
UDC: 512.76
MSC: 14J30, 14E30, 14E05
Language: English
Original paper language: English
Citation: S. Mori, Yu. G. Prokhorov, “Threefold extremal contractions of type (IIA). I”, Izv. Math., 80:5 (2016), 884–909
Citation in format AMSBIB
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\paper Threefold extremal contractions of type (IIA).~I
\jour Izv. Math.
\yr 2016
\vol 80
\issue 5
\pages 884--909
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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