Geodesic
Birational automorphisms of a~three-dimensional double quadric with an~elementary singularity
Sbornik. Mathematics, Tome 189 (1998) no. 1, pp. 97-114

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It is proved that the group of birational automorphisms of a three-dimensional double quadric with a singular point arising from a double point on the branch divisor is a semidirect product of the free group generated by birational involutions of a special form and the group of regular automorphisms. The proof is based on the method of 'untwisting' maximal singularities of linear systems. 
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     author = {M. M. Grinenko},
     title = {Birational automorphisms of a~three-dimensional  double quadric with an~elementary singularity},
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     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_1_a4/}
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M. M. Grinenko. Birational automorphisms of a~three-dimensional  double quadric with an~elementary singularity. Sbornik. Mathematics, Tome 189 (1998) no. 1, pp. 97-114. http://geodesic.mathdoc.fr/item/SM_1998_189_1_a4/