Geodesic
Birational automorphisms of a double space and double quadric
Izvestiya. Mathematics, Tome 32 (1989) no. 1, pp. 233-243 
A. V. Pukhlikov. Birational automorphisms of a double space and double quadric. Izvestiya. Mathematics, Tome 32 (1989) no. 1, pp. 233-243. http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a12/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the groups of birational automorphisms are the same as the groups of biregular automorphisms for two series of Fano varieties of dimension 4 and higher: double spaces of index 1 and double quadrics of index 1. From this it follows that the varieties are not rational. The proof that the respective automorphism groups are the same extends the method of V. A. Iskovskikh and Yu. I. Manin (the method of isolating and excluding maximal singularities) to arbitrary dimension. Bibliography: 7 titles.

[1] Griffits F., Kharris Dzh., Printsipy algebraicheskoi geometrii, Mir, M., 1982 | MR

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

[3] Iskovskikh V. A., “Biratsionalnye avtomorfizmy trekhmernykh algebraicheskikh mnogoobrazie”, Sovremennye problemy matematiki, 12, VINITI, M., 1979, 159–236 | MR

[4] Manin Yu. I., “Sootvetstviya, motivy i monoidalnye preobrazovaniya”, Matem. sb., 77(119) (1968), 475–507 | 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. MGU. Ser. matem., 1986, no. 2, 10–15 | MR | Zbl

[7] Khironaka X., “Razreshenie osobennostei algebraicheskikh mnogoobrazii nad polyami kharakteristiki nul”, Matematika, 9:6 (1965), 3–70; 10:1 (1966), 3–89 ; 10:2 (1966), 3–58 | MR | MR