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Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 5, Pages 77–102 (Mi izv8516)  

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

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

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.


DOI: https://doi.org/10.4213/im8516

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English version:
Izvestiya: Mathematics, 2016, 80:5, 884–909

Bibliographic databases:

ArXiv: 1601.07671
Document Type: Article
UDC: 512.76
MSC: 14J30, 14E30, 14E05
Received: 28.01.2016
Language: English

Citation: S. Mori, Yu. G. Prokhorov, “Threefold extremal contractions of type (IIA). I”, Izv. RAN. Ser. Mat., 80:5 (2016), 77–102; Izv. Math., 80:5 (2016), 884–909

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    This publication is cited in the following articles:
    1. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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