@article{ASNSP_1997_4_24_1_63_0, author = {Kachi, Yasuyuki}, title = {Extremal contractions from $4$-dimensional manifolds to $3$-folds}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {63--131}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 24}, number = {1}, year = {1997}, zbl = {0908.14002}, mrnumber = {1475773}, language = {en}, url = {archive.numdam.org/item/ASNSP_1997_4_24_1_63_0/} }
Kachi, Yasuyuki. Extremal contractions from $4$-dimensional manifolds to $3$-folds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 24 (1997) no. 1, pp. 63-131. http://archive.numdam.org/item/ASNSP_1997_4_24_1_63_0/
[1] On extremal rays of the higher dimensional varieties, Invent. Math. 81 (1985), 347-357. | MR 799271 | Zbl 0554.14001
,[2] A note on nonvanishing and applications, Duke Math. J. 72 (1993), 739-755. | MR 1253623 | Zbl 0853.14003
- ,[3] On good contractions of smooth varieties, preprint (1996). | MR 1620110
- ,[4] Variétés de Prym et Jacobiennes intermédiaires, Ann. Sci. École Norm. Sup. 10 (1977), 309-391. | Numdam | MR 472843 | Zbl 0368.14018
,[5] On d-folds whose canonical bundle is not numerically effective, according to Mori and Kawamata, Ann. Mat. Pura. Appl. 147 (1987), 151-172. | MR 916706 | Zbl 0633.14021
,[6] Connexité rationnelle des variété de Fano, Ann. Sci. École Norm. Sup. 25 (1992), 539-545. | Numdam | MR 1191735 | Zbl 0783.14022
,[7] Decomposition of certain birational morphisms, Math. USSR.-Izv. 16 (1981), 419-429. | Zbl 0464.14003
,[8] On Del Pezzofibrations over curves, Osaka Math. J. 27 (1990), 229-245. | MR 1066621 | Zbl 0715.14030
,[9] Vektorbündel vom rang 2 über dem n-dimensionalen komplex-projektiven raum, Manuscripta. Math. 16 (1975), 75-100. | MR 382278 | Zbl 0318.32027
- ,[10] Generalized adjunction and applications, Math. Proc. Cambridge Philos. Soc. 99 (1986), 457-472. | MR 830359 | Zbl 0619.14004
,[11] Double projection from a line on Fano threefolds of the first kind, Math. USSR.-Sb. 66 (1990), 265-284. | MR 993458 | Zbl 0691.14027
,[12] Elementary contractions of algebraic 3-folds, Ann. of Math. 119 (1984), 95-110. | MR 736561 | Zbl 0542.14007
,[13] The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603-633. | MR 744865 | Zbl 0544.14009
,[14] Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces, Ann. of Math. 127 (1988), 93-163. | MR 924674 | Zbl 0651.14005
,[15] Small contractions of four dimensional algebraic manifolds, Math. Ann. 284 (1989), 595-600. | MR 1006374 | Zbl 0661.14009
,[16] On the length of an extremal rational curve, Invent. Math. 105 (1991), 609-611. | MR 1117153 | Zbl 0751.14007
,[17] Semistable minimal models ofthreefolds in positive or mixed characteristic, J. Alg. Geom. 3 (1994),463-491. | MR 1269717 | Zbl 0823.14026
,[18] Introduction to the minimal model problem, in Algebraic Geometry, Sendai 1985, Adv. Stud. Pure Math. vol. 10 (T. Oda ed.), Kinokuniya, 1987, pp. 283-360. | MR 946243 | Zbl 0672.14006
- - ,[19] Higher direct images of dualizing sheaves I, Ann. of Math. 123 (1986), 11-42. | MR 825838 | Zbl 0598.14015
,[20] Higher direct images of dualizing sheaves II, Ann. of Math. 124 (1986), 171-202. | MR 847955 | Zbl 0605.14014
,[21] Flops, Nagoya Math. J. 113 (1989), 15-36. | MR 986434 | Zbl 0645.14004
,[22] Rational curves on Fano varieties, preprint (1991). | MR 1180339
- - ,[23] Rationally connected varieties, J. Alg. Geom. 1 (1992), 429-448. | MR 1158625 | Zbl 0780.14026
- - ,[24] Rational connectedness and boundedness of Fano manifolds, J. Differential Geom. 36 (1992), 765-779. | MR 1189503 | Zbl 0759.14032
- - ,[25] Classification of three dimensional flips, J. Amer. Math. Soc. 5 (1992), 533-703. | MR 1149195 | Zbl 0773.14004
- ,[26] A numerical criterion for uniruledness, Ann. of Math. 124 (1986), 65-69. | MR 847952 | Zbl 0606.14030
- ,[27] Projective manifolds with ample tangent bundles, Ann. of Math. 110 (1979), 593-606. | MR 554387 | Zbl 0423.14006
,[28] Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982),133-176. | MR 662120 | Zbl 0557.14021
,[29] On 3-dimensional terminal singularities, Nagoya Math. J. 98 (1985), 43-66. | MR 792770 | Zbl 0589.14005
,[30] Flip theorem and the existence of minimal models for 3-folds, J. Amer. Math. Soc. 1 (1988), 117-253. | MR 924704 | Zbl 0649.14023
,[31] On Fano 3-folds with B2 ≽ 2, in Algebraic and Analytic Varieties, Adv. Stud.in Pure Math. vol. 1 (S. Iitaka ed.), Kinokuniys, 1983, pp. 101-129. | Zbl 0537.14026
- ,[32] Classification of Fano 3-folds with B2 ≽ 2, I, Alg. and Top. Theories - to the memory of Dr. T.Miyata, 1985, pp. 496-545. | Zbl 0800.14021
- ,[33] Biregular classification of Fano 3-folds and Fano manifolds of coindex 3, Proc. Nat. Acad. Sci. USA 86 (1989), 3000-3002. | MR 995400 | Zbl 0679.14020
,[34] The lower semi-continuity of the plurigenera of complex varieties, in Algebraic Geometry, Sendai 1985, Adv. St. Pure Math. vol. 10 (T. Oda ed.), Kinokuniya, 1987, pp. 551-590. | MR 946250 | Zbl 0649.14003
,[35] Vector bundles on complex projective spaces, Progress in Math. 3, Birkhäuser, Boston, 1980. | MR 561910 | Zbl 0438.32016
- - ,[36] Factorization of birational maps in dimension 3, Proc. Sympos. Pure Math. 40 (1983), 343-371. | MR 713260 | Zbl 0544.14005
,[37] Lines on Fano 3-folds according to Shokurov, preprint (1980).
,[38] Minimal models of canonical 3-folds, in Algebraic and Analytic Varieties, Adv. Stud. in Pure Math. vol. 1 (S. Iitaka ed.), Kinokuniya, 1983, pp. 131-180. | MR 715649 | Zbl 0558.14028
,[39] Projective morphisms according to Kawamata, preprint (1983). | MR 717617
,[40] On conic bundle structures, Math. USSR. Izv. 20 (1983), 355-390. | MR 651652 | Zbl 0593.14034
,[41] The existence of a straight line on Fano 3-folds, Math. USSR.-Izv. 15 (1980), 173-209. | Zbl 0444.14027
,[42] The nonvanishing theorem, Math. USSR.-Izv. 26 (1986),591-604. | Zbl 0605.14006
,[43] 3-fold log flips, Math. USSR.-Izv. 40 (1993), 95-202. | MR 1162635 | Zbl 0785.14023
,[44] Some birational maps of Fano 3-folds, Compositio Math. 71 (1989),265-283. | Numdam | MR 1022045 | Zbl 0712.14025
,[45] Flips and abundance for algebraic threefolds, Astérisque vol. 211, Soc. Math. de France, 1992. | MR 1225842 | Zbl 0814.14038
et al..,[46] On uniform vector bundles, Math. Ann. 195 (1972), 245-248. | MR 291182 | Zbl 0215.43202
,[47] Fano fourfolds of index greater than one, J. Reine. Angew. Math. 379 (1987), 172-181. | MR 903639 | Zbl 0611.14034
,[48] On contraction of extremal rays of Fano manifolds, J. Reine. Angew. Math. 417 (1991), 141-157. | MR 1103910 | Zbl 0721.14023
,