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This article is cited in 38 scientific papers (total in 38 papers)
Birational automorphisms of a three-dimensional quartic with a quadratic singularity
A. V. Pukhlikov
Abstract:
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.
Received: 02.12.1986
Citation:
A. V. Pukhlikov, “Birational automorphisms of a three-dimensional quartic with a quadratic singularity”, Math. USSR-Sb., 63:2 (1989), 457–482
Linking options:
https://www.mathnet.ru/eng/sm1719https://doi.org/10.1070/SM1989v063n02ABEH003285 https://www.mathnet.ru/eng/sm/v177/i4/p472
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Abstract page: | 419 | Russian version PDF: | 117 | English version PDF: | 16 | References: | 44 | First page: | 1 |
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