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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm5239https://doi.org/10.4213/mzm5239 https://www.mathnet.ru/eng/mzm/v84/i2/p300
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