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Birational rigidity and Q-factoriality of a singular double quadric

Constantin Shramov
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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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Constantin Shramov. 2008-03-30. Birational rigidity and Q-factoriality of a singular double quadric. https://arxiv.org/abs/math/0701522

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