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Sbornik: Mathematics, 2011, Volume 202, Issue 2, Pages 207–241
DOI: https://doi.org/10.1070/SM2011v202n02ABEH004143 (Mi sm7667) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Three-dimensional quartics containing a plane

M. M. Grinenko

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (426 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/SM2011v202n02ABEH004143
Abstract: We study Fano threefolds birationally equivalent to a quartic containing a plane. We prove that linear systems that have no maximal singularities at a singular point of the variety can have maximal singularities only along curves of degree one. We construct corresponding birational automorphisms.
Bibliography: 10 titles.
Keywords: birational geometry, Fano varieties, method of maximal singularities.
Received: 15.12.2009 and 19.07.2010
Bibliographic databases:
Document Type: Article
UDC: 512.763
MSC: 14J30, 14J45
Language: English
Original paper language: Russian
Citation: M. M. Grinenko, “Three-dimensional quartics containing a plane”, Sb. Math., 202:2 (2011), 207–241
Citation in format AMSBIB
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\by M.~M.~Grinenko
\paper Three-dimensional quartics containing a~plane
\jour Sb. Math.
\yr 2011
\vol 202
\issue 2
\pages 207--241
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79955652505}
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  • https://doi.org/10.1070/SM2011v202n02ABEH004143
  • https://www.mathnet.ru/eng/sm/v202/i2/p57
    • This publication is cited in the following 1 articles:
    1. T. Okada, “Birational Mori fiber structures of Q-Fano 3-fold weighted complete intersections”, Proc. London Math. Soc. (3), 109:6 (2014), 1549–1600  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:500
    Russian version PDF:210
    English version PDF:17
    References:64
    First page:8
     
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