Geodesic
Birational automorphisms of a three-dimensional double quadric with an elementary singularity
Sbornik. Mathematics, Tome 189 (1998) no. 1, pp. 97-114 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SM_1998_189_1_a4,
     author = {M. M. Grinenko},
     title = {Birational automorphisms of a~three-dimensional double quadric with an~elementary singularity},
     journal = {Sbornik. Mathematics},
     pages = {97--114},
     year = {1998},
     volume = {189},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_1_a4/}
}
TY  - JOUR
AU  - M. M. Grinenko
TI  - Birational automorphisms of a three-dimensional double quadric with an elementary singularity
JO  - Sbornik. Mathematics
PY  - 1998
SP  - 97
EP  - 114
VL  - 189
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1998_189_1_a4/
LA  - en
ID  - SM_1998_189_1_a4
ER  - 
%0 Journal Article
%A M. M. Grinenko
%T Birational automorphisms of a three-dimensional double quadric with an elementary singularity
%J Sbornik. Mathematics
%D 1998
%P 97-114
%V 189
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1998_189_1_a4/
%G en
%F SM_1998_189_1_a4
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/

[1] Iskovskikh V. A., “Biratsionalnye avtomorfizmy trekhmernykh algebraicheskikh mnogoobrazii”, Itogi nauki i tekhniki. Sovr. probl. matem., 12, VINITI, M., 1979, 159–236 | MR

[2] Iskovskikh V. A., Manin Yu. A., “Trekhmernye kvartiki i kontrprimery k probleme Lyurota”, Matem. sb., 86 (128):1 (1971), 140–166 | MR | Zbl

[3] Pukhlikov A. V., “Biratsionalnye avtomorfizmy trekhmernoi kvartiki s prosteishei osobennostyu”, Matem. sb., 135 (177):4 (1988), 472–496 | MR | Zbl

[4] Pukhlikov A. V., “Biratsionalnye avtomorfizmy dvoinogo prostranstva i dvoinoi kvadriki”, Izv. AN SSSR. Ser. matem., 52:1 (1988), 229–239 | MR

[5] Pukhlikov A. V., Essentials of the method of maximal singularieties, Warwick Preprints: 31/1996 | MR