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Birational rigidity and \(\mathbb Q\)-factoriality of a singular double cover of a quadric branched over a divisor of degree 4. (English. Russian original) Zbl 1219.14014

Math. Notes 84, No. 2, 280-289 (2008); translation from Mat. Zametki 84, No. 2, 300-311 (2008).
Summary: 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.

MSC:

14E05 Rational and birational maps
14E07 Birational automorphisms, Cremona group and generalizations
14E08 Rationality questions in algebraic geometry
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References:

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