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Mat. Zametki, 2008, Volume 84, Issue 2, Pages 300–311 (Mi mz5239)  

This article is cited in 2 scientific papers (total in 2 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

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

DOI: https://doi.org/10.4213/mzm5239

Full text: PDF file (522 kB)
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English version:
Mathematical Notes, 2008, 84:2, 280–289

Bibliographic databases:

UDC: 514
Received: 04.07.2007

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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\by K.~A.~Shramov
\paper Birational Rigidity and $\mathbb Q$-Factoriality of a Singular Double Cover of a Quadric Branched over a Divisor of Degree~4
\jour Mat. Zametki
\yr 2008
\vol 84
\issue 2
\pages 300--311
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\crossref{https://doi.org/10.4213/mzm5239}
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\transl
\jour Math. Notes
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\vol 84
\issue 2
\pages 280--289
\crossref{https://doi.org/10.1134/S0001434608070274}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. Cheltsov I., Przyjalkowski V., Shramov C., “Which Quartic Double Solids Are Rational?”, J. Algebr. Geom., 28:2 (2019), 201–243  crossref  zmath  isi
  • Математические заметки Mathematical Notes
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