Geodesic
Birational automorphisms of a three-dimensional quartic with a quadratic singularity
Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 457-482

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The author studies birational automorphisms of a hypersurface of degree 4 in the four-dimensional projective space over an algebraically closed field having a unique ordinary double point of general type. It is shown that the group of birational automorphisms of a quartic is a semidirect product of a normal subgroup of finite index freely generated by 25 birational involutions and the (finite) group of biregular (projective) automorphisms of the quartic. Such a quartic is not rational. The proof is based on the techniques of maximal singularities due to V. A. Iskovskih and Yu. I. Manin. Bibliography: 7 titles. 
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     author = {A. V. Pukhlikov},
     title = {Birational automorphisms of a three-dimensional quartic with a quadratic singularity},
     journal = {Sbornik. Mathematics},
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     number = {2},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_63_2_a12/}
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A. V. Pukhlikov. Birational automorphisms of a three-dimensional quartic with a quadratic singularity. Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 457-482. http://geodesic.mathdoc.fr/item/SM_1989_63_2_a12/