Geodesic
Birational Rigidity and $\mathbb Q$-Factoriality of a Singular Double Cover of a Quadric Branched over a Divisor of Degree~4
Matematičeskie zametki, Tome 84 (2008) no. 2, pp. 300-311

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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.
Keywords: birational geometry, Mori fibration, birational rigidity, Fano variety, sextic, superrigidity.
Mots-clés : birational automorphism, quartic 
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     author = {K. A. Shramov},
     title = {Birational {Rigidity} and $\mathbb Q${-Factoriality} of a {Singular} {Double} {Cover} of a {Quadric}  {Branched} over a {Divisor} of {Degree~4}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {300--311},
     publisher = {mathdoc},
     volume = {84},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_2_a10/}
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K. A. Shramov. Birational Rigidity and $\mathbb Q$-Factoriality of a Singular Double Cover of a Quadric  Branched over a Divisor of Degree~4. Matematičeskie zametki, Tome 84 (2008) no. 2, pp. 300-311. http://geodesic.mathdoc.fr/item/MZM_2008_84_2_a10/