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Matematicheskie Zametki, 2008, Volume 84, Issue 2, Pages 300–311
DOI: https://doi.org/10.4213/mzm5239
(Mi mzm5239)
 

This article is cited in 3 scientific papers (total in 3 papers)

Birational Rigidity and Q-Factoriality of a Singular Double Cover of a Quadric Branched over a Divisor of Degree 4

K. A. Shramov

M. V. Lomonosov Moscow State University
Full-text PDF (522 kB) Citations (3)
References:
Abstract: We prove birational rigidity and calculate the group of birational automorphisms of a nodal Q-factorial double cover X of a smooth three-dimensional quadric branched over a quartic section. We also prove that X is Q-factorial provided that it has at most 11 singularities; moreover, we give an example of a non-Q-factorial variety of this type with 12 simple double singularities.
Keywords: birational geometry, Mori fibration, birational automorphism, birational rigidity, Fano variety, quartic, sextic, superrigidity.
Received: 04.07.2007
English version:
Mathematical Notes, 2008, Volume 84, Issue 2, Pages 280–289
DOI: https://doi.org/10.1134/S0001434608070274
Bibliographic databases:
Document Type: Article
UDC: 514
Language: Russian
Citation: K. A. Shramov, “Birational Rigidity and Q-Factoriality of a Singular Double Cover of a Quadric Branched over a Divisor of Degree 4”, Mat. Zametki, 84:2 (2008), 300–311; Math. Notes, 84:2 (2008), 280–289
Citation in format AMSBIB
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\pages 300--311
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Linking options:
  • https://www.mathnet.ru/eng/mzm5239
  • https://doi.org/10.4213/mzm5239
  • https://www.mathnet.ru/eng/mzm/v84/i2/p300
  • This publication is cited in the following 3 articles:
    1. Cheltsov I. Kuznetsov A. Shramov C., “Coble Fourfold, S-6-Invariant Quartic Threefolds, and Wiman-Edge Sextics”, Algebr. Number Theory, 14:1 (2020), 213–274  crossref  mathscinet  isi
    2. Cheltsov I., Przyjalkowski V., Shramov C., “Which Quartic Double Solids Are Rational?”, J. Algebr. Geom., 28:2 (2019), 201–243  crossref  mathscinet  zmath  isi
    3. Victor V. Przyjalkowski, Constantin A. Shramov, “Double quadrics with large automorphism groups”, Proc. Steklov Inst. Math., 294 (2016), 154–175  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:78
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