Geodesic
Birational automorphisms of a three-dimensional quartic with a quadratic singularity
Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 457-482 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SM_1989_63_2_a12,
     author = {A. V. Pukhlikov},
     title = {Birational automorphisms of a three-dimensional quartic with a quadratic singularity},
     journal = {Sbornik. Mathematics},
     pages = {457--482},
     year = {1989},
     volume = {63},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_63_2_a12/}
}
TY  - JOUR
AU  - A. V. Pukhlikov
TI  - Birational automorphisms of a three-dimensional quartic with a quadratic singularity
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 457
EP  - 482
VL  - 63
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1989_63_2_a12/
LA  - en
ID  - SM_1989_63_2_a12
ER  - 
%0 Journal Article
%A A. V. Pukhlikov
%T Birational automorphisms of a three-dimensional quartic with a quadratic singularity
%J Sbornik. Mathematics
%D 1989
%P 457-482
%V 63
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1989_63_2_a12/
%G en
%F SM_1989_63_2_a12
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/

[1] Iskovskikh V. A., “Antikanonicheskie modeli trekhmernykh algebraicheskikh mnogoobrazii”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 12, VINITI, M., 1979, 59–157 | MR

[2] Iskovskikh V. A., “Biratsionalnye avtomorfizmy trekhmernykh algebraicheskikh mnogoobrazii”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 12, VINITI, M., 1979, 159–236 | MR

[3] Iskovskikh V. A., “O biratsionalnykh avtomorfizmakh trekhmernykh algebraicheskikh mnogoobrazii”, DAN SSSR, 235:3 (1977), 509–511 | MR | Zbl

[4] Iskovskikh V. A., Manin Yu. I., “Trekhmernye kvartiki i kontrprimery k probleme Lyurota”, Matem. sb., 86(128) (1971), 140–166 | MR | Zbl

[5] Manin Yu. I., “Lektsii o $K$-funktore v algebraicheskoi geometrii”, UMN, 24:5 (1969), 3–86 | MR | Zbl

[6] Pukhlikov A. V., “Biratsionalnye avtomorfizmy chetyrekhmernoi kvintiki”, Vestn. Mosk. un-ta. Ser. 1, 1986, no. 2, 10–15 | MR | Zbl

[7] Khashin S. I., “Biratsionalnye avtomorfizmy dvoinogo konusa razmernosti tri”, Vestn. Mosk. un-ta. Ser. 1, 1984, no. 1, 21–26 | MR