@article{LKN_2015_24_24_a0,
author = {Yu. G. Prokhorov},
title = {Rational surfaces},
journal = {Lekcionnye kursy NOC},
pages = {3--76},
year = {2015},
volume = {24},
number = {24},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/LKN_2015_24_24_a0/}
}
Yu. G. Prokhorov. Rational surfaces. Lekcionnye kursy NOC, Rational surfaces, Tome 24 (2015) no. 24, pp. 3-76. http://geodesic.mathdoc.fr/item/LKN_2015_24_24_a0/
[1] Ju. I. Manin, “Ratsionalnye poverkhnosti nad sovershennymi polyami”, Inst. Hautes Études Sci. Publ. Math., 1966, no. 30, 55–97 | DOI | MR | Zbl
[2] S. Mori, “Threefolds whose canonical bundles are not numerically effective”, Ann. of Math. (2), 115 (1982), 133–176 | DOI | MR | Zbl
[3] Kh. Klemens, Ya. Kollar, S. Mori, Mnogomernaya kompleksnaya geometriya, Mir, M., 1993 | Zbl
[4] Yu. Prokhorov, “$G$-Fano threefolds. I”, Adv. Geom., 13:3 (2013), 389–418 | DOI | MR | Zbl
[5] Yu. Prokhorov, “$G$-Fano threefolds. II”, Adv. Geom., 13:3 (2013), 419–434 | DOI | MR | Zbl
[6] Yu. I. Manin, Kubicheskie formy. Algebra, geometriya, arifmetika, Nauka, M., 1972 | MR | Zbl
[7] C. Salgado, D. Testa, A. Várilly-Alvarado, Anthony, “On the unirationality of del Pezzo surfaces of degree 2”, J. Lond. Math. Soc. (2), 90:1 (2014), 121–139 | DOI | MR | Zbl
[8] V. A. Iskovskikh, “Ratsionalnye poverkhnosti s puchkom ratsionalnykh krivykh”, Matem. sb., 74:4 (1967), 608–638 | MR | Zbl
[9] V. A. Iskovskikh, “Ratsionalnye poverkhnosti s puchkom ratsionalnykh krivykh i s polozhitelnym kvadratom kanonicheskogo klassa”, Matem. sb., 83:1 (1970), 90–119 | MR | Zbl
[10] V. A. Iskovskikh, “Minimalnye modeli ratsionalnykh poverkhnostei nad proizvolnymi polyami”, Izv. AN SSSR. Ser. matem., 43:1 (1979), 19–43 | MR | Zbl
[11] V. A. Iskovskikh, “Faktorizatsiya biratsionalnykh otobrazhenii ratsionalnykh poverkhnostei s tochki zreniya teorii Mori”, UMN, 51:4 (1996), 3–72 | DOI | MR | Zbl
[12] I. R. Shafarevich, Osnovy algebraicheskoi geometrii. T. 1. Algebraicheskie mnogoobraziya v proektivnom prostranstve, Nauka, M., 1988 | MR | Zbl
[13] R. Khartskhorn, Algebraicheskaya geometriya, Mir, M., 1981 | MR | Zbl
[14] I. R. Shafarevich, B. G. Averbukh, Yu. R. Vainberg, A. B. Zhizhchenko, Yu. I. Manin, B. G. Moishezon, G. N. Tyurina, A. N. Tyurin, “Algebraicheskie poverkhnosti”, Tr. MIAN SSSR, 75, Nauka, M., 1965, 3–215 | MR | Zbl
[15] V. A. Iskovskikh, I. R. Shafarevich, “Algebraicheskie poverkhnosti”, Algebraicheskaya geometriya – 2, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 35, VINITI, M., 1989, 131–263 | MR | Zbl
[16] A. Beauville, Surfaces algébriques complexes, Astérisque, 54, Soc. Math. France, Paris, 1978 | MR
[17] M. Reid, “Chapters on algebraic surfaces”, Complex Algebraic Geometry, IAS/Park City Math. Ser., 3, Amer. Math. Soc., Providence, RI, 1997, 3–159 | MR | Zbl
[18] J. Kollár, Rational Curves on Algebraic Varieties, Ergeb. Math. Grenzgeb. (3), 32, Springer-Verlag, Berlin, 1996 | MR
[19] Yu. I. Manin, M. A. Tsfasman, “Ratsionalnye mnogoobraziya: algebra, geometriya, arifmetika”, UMN, 41:2 (1986), 43–94 | MR | Zbl
[20] Dzh. Miln, Etalnye kogomologii, Mir, M., 1983 | MR | Zbl
[21] J.-P. Serre, “Morphismes universels et variétés d'Albanese”, Variétés de Picard, Sém. C. Chevalley, 3, 1958/59, no. 10, 1960 | Zbl
[22] D. Mamford, Lektsii o krivykh na algebraicheskoi poverkhnosti, Mir, M., 1968 | MR | Zbl
[23] A. Grothendieck, “Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. II”, Inst. Hautes Études Sci. Publ. Math., 1965, no. 24, 1–231 | MR | Zbl
[24] A. Grothendieck, “Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. III”, Inst. Hautes Études Sci. Publ. Math., 1966, no. 28, 1–255 | MR | Zbl
[25] I. V. Dolgachev, V. A. Iskovskikh, “Finite subgroups of the plane Cremona group”, Algebra, Arithmetic, and Geometry: in Honor of Yu. I. Manin, Vol. I, Progr. Math., 269, Birkhäuser Boston, Boston, MA, 2009, 443–548 | DOI | MR | Zbl
[26] I. V. Dolgachev, Classical Algebraic Geometry. A Modern View, Cambridge Univ. Press, Cambridge, 2012 | DOI | MR | Zbl
[27] V. A. Iskovskikh, Yu. Prokhorov, Algebraic Geometry. V. Fano Varieties, Encyclopaedia Math. Sci., 47, Springer-Verlag, Berlin, 1999 | MR | Zbl
[28] F. Griffits, Dzh. Kharris, Printsipy algbraicheskoi geometrii, T. 1, 2, Mir, M., 1982 | MR | Zbl
[29] I. V. Dolgachev, “On Elements of Order $p^s$ in the Plane Cremona Group over a Field of Characteristic $p$”, Mnogomernaya algebraicheskaya geometriya, Tr. MIAN, 264, MAIK, M., 2009, 55–62 | MR
[30] Zh.-P. Serr, Kurs arifmetiki, Mir, M., 1972 | MR | Zbl
[31] Yu. G. Prokhorov, Osobennosti algebraicheskikh mnogoobrazii, MTsNMO, M., 2009
[32] N. Burbaki, Gruppy i algebry Li. Gl. 4–6. Gruppy Kokstera i sistemy Titsa. Gruppy, porozhdennye otrazheniyami. Sistemy kornei, Elementy matematiki, Mir, M., 1972 | MR | Zbl
[33] I. V. Dolgachev, “Finite subgroups of the plane Cremona group”, Algebraic geometry in East Asia—Seoul 2008, Adv. Stud. Pure Math., 60, Math. Soc. Japan, Tokyo, 2010, 1–49 | MR | Zbl
[34] N. I. Shepherd-Barron, “The rationality of quintic Del Pezzo surfaces—a short proof”, Bull. London Math. Soc., 24:3 (1992), 249–250 | DOI | MR | Zbl
[35] U. Fulton, Teoriya peresechenii, Mir, M., 1989 | MR | Zbl
[36] J. Kollár, “Unirationality of cubic hypersurfaces”, J. Inst. Math. Jussieu, 1:3 (2002), 467–476 | MR | Zbl
[37] A. V. Voskresenskii, Algebraicheskie tory, Nauka, M., 1977 | MR | Zbl
[38] V. A. Iskovskikh, “Two non-conjugate embeddings of $S_3\times Z_2$ into the Cremona group. II”, Algebraic geometry in East Asia—Hanoi 2005, Adv. Stud. Pure Math., 50, Math. Soc. Japan, Tokyo, 2008, 251–267 | MR | Zbl
[39] A. Corti, “Factoring birational maps of threefolds after Sarkisov”, J. Algebraic Geom., 4:2 (1995), 223–254 | MR | Zbl
[40] W. van der Kulk, “On polynomial rings in two variables”, Nieuw Arch. Wiskunde (3), 1 (1953), 33–41 | MR | Zbl
[41] M. Kh. Gizatullin, “Opredelyayuschie sootnosheniya dlya kremonovoi gruppy ploskosti”, Izv. AN SSSR. Ser. matem., 46:5 (1982), 909–970 | MR | Zbl
[42] V. A. Iskovskikh, “Prostoe dokazatelstvo teoremy Gizatullina”, Teoriya Galua, koltsa, algebraicheskie gruppy i ikh prilozheniya, Tr. MIAN SSSR, 183, Nauka. Leningradskoe otd., L., 1990, 111–116 | MR | Zbl
[43] V. A. Iskovskikh, “Obrazuyuschie v dvumernoi gruppe Kremony nad nezamknutym polem”, Teoriya chisel, algebra, matematicheskii analiz i ikh prilozheniya, Tr. MIAN, 200, Nauka, M., 1991, 157–170 | MR | Zbl
[44] V. A. Iskovskikh, F. K. Kabdykairov, S. L. Tregub, “Sootnosheniya v dvumernoi gruppe Kremony nad sovershennym polem”, Izv. RAN. Ser. matem., 57:3 (1993), 3–69 | MR | Zbl
[45] L. Bayle, A. Beauville, “Birational involutions of $\mathbb P_2$”, Asian J. Math., 4:1 (2000), 11–17 | MR | Zbl
[46] T. de Fernex, “On planar Cremona maps of prime order”, Nagoya Math. J., 174 (2004), 1–28 | MR | Zbl
[47] J. Blanc, “Linearisation of finite abelian subgroups of the Cremona group of the plane”, Groups Geom. Dyn., 3:2 (2009), 215–266 | DOI | MR | Zbl