Birational rigidity and Q-factoriality of a singular double quadric

Details Birational rigidity and Q-factoriality of a singular double quadric Birational rigidity and Q-factoriality of a singular double quadric

2007-01-18

arxiv.org/abs/math/0701522v2

Mathematics

Algebraic Geometry

14 pages; minor corrections

Scientific paper

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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