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.
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Original Russian Text © K. A. Shramov, 2008, published in Matematicheskie Zametki, 2008, Vol. 84, No. 2, pp. 300–311
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Shramov, K.A. Birational rigidity and ℚ-factoriality of a singular double cover of a quadric branched over a divisor of degree 4. Math Notes 84, 280–289 (2008). https://doi.org/10.1134/S0001434608070274
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DOI: https://doi.org/10.1134/S0001434608070274