Birational rigidity and ℚ-factoriality of a singular double cover of a quadric branched over a divisor of degree 4
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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.
Key wordsbirational geometry Mori fibration birational automorphism birational rigidity Fano variety quartic sextic superrigidity
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