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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 3, Pages 158–212 (Mi izv8833)  

Threefold extremal curve germs with one non-Gorenstein point

Sh. Moriab, Yu. G. Prokhorovcde

a Kyoto University Institute for Advanced Study, Kyoto University, Kyoto, Japan
b Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
d Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
e National Research University "Higher School of Economics", Moscow

Abstract: An extremal curve germ is the analytic germ of a threefold with terminal singularities along a reduced complete curve admitting a contraction whose fibres have dimension at most one. The aim of the present paper is to review the results concerning contractions whose central fibre is irreducible and contains only one non-Gorenstein point.

Keywords: extremal curve germ, terminal singularity, canonical divisor, birational map, blow-up, flip, $Q$-conic bundle.

Funding Agency Grant Number
Japan Society for the Promotion of Science JP25287005
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01
Ministry of Education and Science of the Russian Federation 5-100
This work was supported by the Research Institute for Mathematical Sciences, a Joint Usage/Research centre located in Kyoto University. The first author was supported by a JSPS grant no. JP25287005. The second author was supported by the Programme of the Presidium of the Russian Academy of Sciences no. 01 ‘Fundamental mathematics and its applications’ under grant PRAS-18-01 and the Russian Academic Excellence Project ‘5-100’.


DOI: https://doi.org/10.4213/im8833

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English version:
Izvestiya: Mathematics, 2019, 83:3, 565–612

Document Type: Article
UDC: 512.776
MSC: 14E05, 14E30, 14J17, 14J30
Received: 28.06.2018

Citation: Sh. Mori, Yu. G. Prokhorov, “Threefold extremal curve germs with one non-Gorenstein point”, Izv. RAN. Ser. Mat., 83:3 (2019), 158–212; Izv. Math., 83:3 (2019), 565–612

Citation in format AMSBIB
\Bibitem{MorPro19}
\by Sh.~Mori, Yu.~G.~Prokhorov
\paper Threefold extremal curve germs with one non-Gorenstein point
\jour Izv. RAN. Ser. Mat.
\yr 2019
\vol 83
\issue 3
\pages 158--212
\mathnet{http://mi.mathnet.ru/izv8833}
\crossref{https://doi.org/10.4213/im8833}
\transl
\jour Izv. Math.
\yr 2019
\vol 83
\issue 3
\pages 565--612
\crossref{https://doi.org/10.1070/IM8833}


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