Factorization of birational maps of rational surfaces from the viewpoint of Mori theory

V. A. Iskovskikh

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 51 (1996) no. 4, pp. 585-652

Bibliographie

[1] Gizatullin M. Kh., “Opredelyayuschie sootnosheniya dlya kremonovoi gruppy ploskosti”, Izv. AN SSSR. Ser. matem., 46:5 (1982), 909–970 | MR | Zbl

[2] Iskovskikh V. A., “O biratsionalnykh formakh ratsionalnykh poverkhnostei”, Izv. AN SSSR. Ser. matem., 29:6 (1965), 1417–1433 | MR | Zbl

[3] Iskovskikh V. A., “Ratsionalnye poverkhnosti s puchkom ratsionalnykh krivykh”, Matem. sb., 74 (116):4 (1967), 608–638 | MR | Zbl

[4] Iskovskikh V. A., “Ratsionalnye poverkhnosti s puchkom ratsionalnykh krivykh i s polozhitelnym kvadratom kanonicheskogo klassa”, Matem. sb., 83 (125):1 (1970), 90–119 | Zbl

[5] Iskovskikh V. A., “Biratsionalnye svoistva poverkhnosti stepeni $4$ v $\mathbb P^4$”, Matem. sb., 88 (130):1 (1972), 31–37 | Zbl

[6] Iskovskikh V. A., “Minimalnye modeli ratsionalnykh poverkhnostei nad proizvolnymi polyami”, Izv. AN SSSR. Ser. matem., 43:1 (1979), 19–43 | MR | Zbl

[7] Iskovskikh V. A., “Biratsionalnye avtomorfizmy trekhmernykh algebraicheskikh mnogoobrazii”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 12, VINITI, M., 1979, 159–235 | MR

[8] Iskovskikh V. A., “Obrazuyuschie i sootnosheniya v gruppakh biratsionalnykh avtomorfizmov dvukh klassov ratsionalnykh poverkhnostei”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 165, 1984, 67–78 | MR | Zbl

[9] Iskovskikh V. A., “Dokazatelstvo teoremy o sootnosheniyakh v dvumernoi gruppe Kremony nad nezamknutym polem”, UMN, 40:5 (245) (1985), 255–256 | MR | Zbl

[10] Iskovskikh V. A., “Prostoe dokazatelstvo teoremy Gizatullina o sootnosheniyakh v dvumernoi gruppe Kremony”, Tr. MIAN, 183, 1990, 111–116 | MR | Zbl

[11] Iskovskikh V. A., “Obrazuyuschie v dvumernoi gruppe Kremony nad nezamknutym polem”, Tr. MIAN, 200, 1991, 157–170 | Zbl

[12] Iskovskikh V. A., “O probleme ratsionalnosti dlya trekhmernykh algebraicheskikh mnogoobrazii, rassloennykh na poverkhnosti Del Petstso”, Tr. MIRAN, 208, 1995, 128–138 | MR | Zbl

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

[14] Iskovskikh V. A., Tregub S. L., “O biratsionalnykh avtomorfizmakh ratsionalnykh poverkhnostei”, Izv. AN SSSR. Ser. matem., 55:2 (1991), 254–281 | MR | Zbl

[15] Iskovskikh V. A., Kabdykirov F. K., Tregub S. L., “Sootnosheniya v dvumernoi gruppe Kremony nad sovershennym polem”, Izv. RAN. Ser. matem., 57:3 (1993), 3–69 | MR | Zbl

[16] Manin Yu. I., “Ratsionalnye poverkhnosti nad sovershennymi polyami”, Publ. Math. IHES, 30 (1966), 55–113 | MR

[17] Manin Yu. I., “Ratsionalnye poverkhnosti nad sovershennymi polyami, II”, Matem. sb., 72 (114) (1967), 161–192 | MR | Zbl

[18] Manin Yu. I., Kubicheskie formy, Nauka, M., 1972

[19] Manin Yu. I., Tsfasman M. A., “Ratsionalnye mnogoobraziya: algebra, geometriya, arifmetika”, UMN, 41:2 (1986), 43–94 | MR | Zbl

[20] Sarkisov V. G., “Biratsionalnye avtomorfizmy rassloenii na koniki”, Izv. AN SSSR. Ser. matem., 44:4 (1980), 818–944 | MR

[21] Corti A., “Factoring birational maps of threefolds after Sarkisov”, J. Alg. Geom., 4 (1995), 223–254 | MR | Zbl

[22] Fano G., “Osservazioni sopra alqune varieta algebriche non razionali aventi tutti i deneri nulli”, Atti Acc. Torino, 50 (1915), 1067–1072

[23] Fano G., “Nuove ricerche sulle varieta algebraiche a tre dimensioni a curve-sezione canoniche”, Pont. Acad. Sci. Comment., 11 (1947), 635–720 | MR | Zbl

[24] Hudson H., Cremona transformation in plane and space, Cambridge Univ. Press, Cambridge, 1927

[25] Kantor R., “Rational Zerlegung der birationalen Transformationen in ihre Primfactoren”, Monatsh. Math. and Phys., 10:1 (1988), 54–74 | DOI | MR

[26] Mori S., “Treefolds whose canonical bundles are not numerically effective”, Ann. Math., 115 (1982), 133–176 | DOI

[27] Sarkisov V. G., Birational maps of standart $Q$-Fano fiberings, Prepr. Kurchatov Inst. Atom. Energy, 1989

[28] Shepherd-Barron N. I., “The Rationality of quintic Del Pezzo surfaces – a short proof”, Bull. London Math. Soc., 24:3 (1992), 249–250 | DOI | MR | Zbl

[29] Swinnerton-Dyer H. P. F., “Rational points on del Pezzo surfaces of degree $5$”, Algebraic geometry (Oslo, 1970), Wolters and Noordhoff, Gronningen, 1972, 287–290 | MR

[30] Reid M., Birational geometry of $3$-folds according to Sarkissov, Prepr. Univ. Warwick, 1991

[31] Roth L., Algebraic threefolds with special regard to problems of rationality, Springer-Verlag, Berlin, 1955

[32] Weinstein F. W., On birational automorphisms of Severi-Brauer surfaces, Prepr. Rep. Math. Univ. Stockholm, No 1, 1989, p. 1–14 | MR

[33] Zariski O., Algebraic surfaces and Edition, Springer-Verlag, Berlin, 1971 | Zbl