Journal of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Browser Compatibility Info Help
ISSN 1088-6834(online) ISSN 0894-0347(print)

Flip theorem and the existence of minimal models for -folds

Author: Shigefumi Mori
Journal: J. Amer. Math. Soc. 1 (1988), 117-253
MSC: Primary 14J30; Secondary 14E35
MathSciNet review: 924704
Full-text PDF Free Access

[A1] M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277–291. MR 0232018 (38 #344)
[A2] M. Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 23–58. MR 0268188 (42 #3087)
[B1] X. Benveniste, Sur l’anneau canonique de certaines variétés de dimension 3, Invent. Math. 73 (1983), no. 1, 157–164 (French). MR 707354 (85g:14020), http://dx.doi.org/10.1007/BF01393831
[B2] X. Benveniste, Sur le cone des 1-cycles effectifs en dimension 3, Math. Ann. 272 (1985), no. 2, 257–265 (French). MR 796252 (86j:14005), http://dx.doi.org/10.1007/BF01450570
[BS] Jürgen Bingener and Uwe Storch, Zur Berechnung der Divisorenklassengruppen kompletter lokaler Ringe, Nova Acta Leopoldina (N.F.) 52 (1981), no. 240, 7–63 (German). Leopoldina Symposium: Singularities (Thüringen, 1978). MR 642696 (83m:13017)
[Da] V. I. Danilov, Birational geometry of toric -folds, Math. USSR-Izv. 21 (1983), 269-279.
[El1] Renée Elkik, Singularités rationnelles et déformations, Invent. Math. 47 (1978), no. 2, 139–147 (French). MR 501926 (80c:14004), http://dx.doi.org/10.1007/BF01578068
[El2] Renée Elkik, Rationalité des singularités canoniques, Invent. Math. 64 (1981), no. 1, 1–6 (French). MR 621766 (83a:14003), http://dx.doi.org/10.1007/BF01393930
[Fl] Hubert Flenner, Rationale quasihomogene Singularitäten, Arch. Math. (Basel) 36 (1981), no. 1, 35–44 (German). MR 612234 (82g:14036), http://dx.doi.org/10.1007/BF01223666
[Fr] P. Francia, Some remarks on minimal models. I, Compositio Math. 40 (1980), no. 3, 301–313. MR 571052 (81h:14013)
[Ft] Takao Fujita, Zariski decomposition and canonical rings of elliptic threefolds, J. Math. Soc. Japan 38 (1986), no. 1, 19–37. MR 816221 (87e:14036), http://dx.doi.org/10.2969/jmsj/03810019
[Go] Roger Godement, Topologie algébrique et théorie des faisceaux, Actualit’es Sci. Ind. No. 1252. Publ. Math. Univ. Strasbourg. No. 13, Hermann, Paris, 1958 (French). MR 0102797 (21 #1583)
[Gra] Hans Grauert, On Levi’s problem and the imbedding of real-analytic manifolds, Ann. of Math. (2) 68 (1958), 460–472. MR 0098847 (20 #5299)
[GR] Hans Grauert and Oswald Riemenschneider, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen, Invent. Math. 11 (1970), 263–292 (German). MR 0302938 (46 #2081)
[Gro] A. Grothendieck, Eléments de géométrie algébrique. III, Inst. Hautes Études Sci. Publ. Math. 20 (1964).
[H] H. Hironaka, On the theory of birational blowing-up, Thesis, Harvard Univ., 1960.
[I] V. A. Iskovskih, Minimal models of rational surfaces over arbitrary fields, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), no. 1, 19–43, 237 (Russian). MR 525940 (80m:14021)
[Ka1] Yujiro Kawamata, On the finiteness of generators of a pluricanonical ring for a 3-fold of general type, Amer. J. Math. 106 (1984), no. 6, 1503–1512. MR 765589 (86j:14032), http://dx.doi.org/10.2307/2374403
[Ka2] -, The crepant blowing-ups of -dimensional canonical singularities and its application to degenerations of surfaces, Ann. of Math. (to appear).
[KMM] Yujiro Kawamata, Katsumi Matsuda, and Kenji Matsuki, Introduction to the minimal model problem, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 283–360. MR 946243 (89e:14015)
[K1] Steven L. Kleiman, Toward a numerical theory of ampleness, Ann. of Math. (2) 84 (1966), 293–344. MR 0206009 (34 #5834)
[Ko1] János Kollár, Higher direct images of dualizing sheaves. I, Ann. of Math. (2) 123 (1986), no. 1, 11–42. MR 825838 (87c:14038), http://dx.doi.org/10.2307/1971351
[Ko2] -, The structure of algebraic threefolds--an introduction to Mori's program, Bull. Amer. Math. Soc. 17 (1987), 215-277.
[Ko3] János Kollár, Flops, Nagoya Math. J. 113 (1989), 15–36. MR 986434 (90e:14011)
[KSB] J. Kollár and N. Shepherd-Barron, Threefolds and deformation of surface singularities, Preprint.
[Ku] Vik. S. Kulikov, Degenerations of 𝐾3 surfaces and Enriques surfaces, Uspehi Mat. Nauk 32 (1977), no. 3(195), 167–168 (Russian). MR 0506295 (58 #22087a)
[Ma] Ju. I. Manin, Rational surfaces over perfect fields, Inst. Hautes Études Sci. Publ. Math. 30 (1966), 55–113 (Russian, with English summary). MR 0225780 (37 #1373)
[Mn] Masayoshi Miyanishi, Projective degenerations of surfaces according to S. Tsunoda, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 415–447. MR 946246 (89k:14021)
[My1] Yoichi Miyaoka, Deformations of a morphism along a foliation and applications, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp. 245–268. MR 927960 (89e:14011)
[My2] Yoichi Miyaoka, The Chern classes and Kodaira dimension of a minimal variety, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 449–476. MR 946247 (89k:14022)
[My3] -, On the Kodaira dimension of Minimal Threefolds, Preprint.
[MM] Yoichi Miyaoka and Shigefumi Mori, A numerical criterion for uniruledness, Ann. of Math. (2) 124 (1986), no. 1, 65–69. MR 847952 (87k:14046), http://dx.doi.org/10.2307/1971387
[Mr1] Shigefumi Mori, Projective manifolds with ample tangent bundles, Ann. of Math. (2) 110 (1979), no. 3, 593–606. MR 554387 (81j:14010), http://dx.doi.org/10.2307/1971241
[Mr2] Shigefumi Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. (2) 116 (1982), no. 1, 133–176. MR 662120 (84e:14032), http://dx.doi.org/10.2307/2007050
[Mr3] Shigefumi Mori, On 3-dimensional terminal singularities, Nagoya Math. J. 98 (1985), 43–66. MR 792770 (86m:14003)
[Mr4] Shigefumi Mori, Classification of higher-dimensional varieties, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp. 269–331. MR 927961 (89a:14040)
[Mrr1] David R. Morrison, Semistable degenerations of Enriques’ and hyperelliptic surfaces, Duke Math. J. 48 (1981), no. 1, 197–249. MR 610184 (82m:14020)
[Mrr2] David R. Morrison, A remark on: “On the plurigenera of minimal algebraic 3-folds with 𝐾\raise3.25pt∼≈\𝑝ℎ𝑎𝑛𝑡𝑜𝑚{≈}0” [Math. Ann. 275 (1986), no. 4, 539–546; MR0859328 (88c:14049)] by Y. Kawamata, Math. Ann. 275 (1986), no. 4, 547–553. MR 859329 (88c:14050), http://dx.doi.org/10.1007/BF01459136
[MS] David R. Morrison and Glenn Stevens, Terminal quotient singularities in dimensions three and four, Proc. Amer. Math. Soc. 90 (1984), no. 1, 15–20. MR 722406 (85a:14004), http://dx.doi.org/10.1090/S0002-9939-1984-0722406-4
[N] Noboru Nakayama, Invariance of the plurigenera of algebraic varieties under minimal model conjectures, Topology 25 (1986), no. 2, 237–251. MR 837624 (87g:14034), http://dx.doi.org/10.1016/0040-9383(86)90042-X
[PP] Ulf Persson and Henry Pinkham, Degeneration of surfaces with trivial canonical bundle, Ann. of Math. (2) 113 (1981), no. 1, 45–66. MR 604042 (82f:14030), http://dx.doi.org/10.2307/1971133
[R1] Miles Reid, Minimal models of canonical 3-folds, Algebraic varieties and analytic varieties (Tokyo, 1981) Adv. Stud. Pure Math., vol. 1, North-Holland, Amsterdam, 1983, pp. 131–180. MR 715649 (86a:14010)
[R2] Miles Reid, Decomposition of toric morphisms, Arithmetic and geometry, Vol. II, Progr. Math., vol. 36, Birkhäuser Boston, Boston, MA, 1983, pp. 395–418. MR 717617 (85e:14071)
[R3] Miles Reid, Tendencious survey of 3-folds, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp. 333–344. MR 927962 (89h:14033)
[R4] -, Young person's guide to canonical singularities, Proc. Sympos. Pure Math. (Summer Research Inst., Bowdoin, 1985), Vol. 46 (1987), pp. 345-414.
[SB] N. Shepherd-Barron, Some questions on singularities in 2 and 3 dimensions, Thesis, Univ. of Warwick, 1980.
[Sh] V. V. Shokurov, A nonvanishing theorem, Izv. Akad. Nauk SSSR Ser. Mat. 49 (1985), no. 3, 635–651 (Russian). MR 794958 (87j:14016)
[T] Shuichiro Tsunoda, Degenerations of surfaces, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 755–764. MR 946256 (90d:14037)
[Wa] Jonathan M. Wahl, Equisingular deformations of normal surface singularities. I, Ann. of Math. (2) 104 (1976), no. 2, 325–356. MR 0422270 (54 #10261)
[Wi] P. M. H. Wilson, Towards birational classification of algebraic varieties, Bull. London Math. Soc. 19 (1987), no. 1, 1–48. MR 865038 (87m:14038), http://dx.doi.org/10.1112/blms/19.1.1

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|