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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 $\mathbb Q$-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 $\mathbb Q$-factorial double cover $X$ of a smooth three-dimensional quadric branched over a quartic section. We also prove that $X$ is $\mathbb Q$-factorial provided that it has at most 11 singularities; moreover, we give an example of a non-$\mathbb Q$-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 $\mathbb Q$-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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\paper Birational Rigidity and $\mathbb Q$-Factoriality of a Singular Double Cover of a Quadric Branched over a Divisor of Degree~4
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\pages 300--311
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  • https://doi.org/10.4213/mzm5239
  • https://www.mathnet.ru/eng/mzm/v84/i2/p300
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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