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.
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
\Bibitem{Shr08}
\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
\yr 2008
\vol 84
\issue 2
\pages 280--289
\crossref{https://doi.org/10.1134/S0001434608070274}
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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:
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
Cheltsov I., Przyjalkowski V., Shramov C., “Which Quartic Double Solids Are Rational?”, J. Algebr. Geom., 28:2 (2019), 201–243
Victor V. Przyjalkowski, Constantin A. Shramov, “Double quadrics with large automorphism groups”, Proc. Steklov Inst. Math., 294 (2016), 154–175