Extremal contractions from 4-dimensional manifolds to 3-folds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 24 (1997) no. 1, p. 63-131
@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},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 24},
     number = {1},
     year = {1997},
     pages = {63-131},
     zbl = {0908.14002},
     mrnumber = {1475773},
     language = {en},
     url = {http://www.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, Serie 4, Volume 24 (1997) no. 1, pp. 63-131. http://www.numdam.org/item/ASNSP_1997_4_24_1_63_0/

[1] T. Ando, On extremal rays of the higher dimensional varieties, Invent. Math. 81 (1985), 347-357. | MR 799271 | Zbl 0554.14001

[2] M. Andreatta - J. Wi, A note on nonvanishing and applications, Duke Math. J. 72 (1993), 739-755. | MR 1253623 | Zbl 0853.14003

[3] M. Andreatta - J. Wi, On good contractions of smooth varieties, preprint (1996). | MR 1620110

[4] A. Beauville, Variétés de Prym et Jacobiennes intermédiaires, Ann. Sci. École Norm. Sup. 10 (1977), 309-391. | Numdam | MR 472843 | Zbl 0368.14018

[5] M. Beltrametti, 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] F. Campana, Connexité rationnelle des variété de Fano, Ann. Sci. École Norm. Sup. 25 (1992), 539-545. | Numdam | MR 1191735 | Zbl 0783.14022

[7] V.I. Danilov, Decomposition of certain birational morphisms, Math. USSR.-Izv. 16 (1981), 419-429. | Zbl 0464.14003

[8] T. Fujita, On Del Pezzofibrations over curves, Osaka Math. J. 27 (1990), 229-245. | MR 1066621 | Zbl 0715.14030

[9] H. Grauert - G. Mülich, Vektorbündel vom rang 2 über dem n-dimensionalen komplex-projektiven raum, Manuscripta. Math. 16 (1975), 75-100. | MR 382278 | Zbl 0318.32027

[10] P. Ionescu, Generalized adjunction and applications, Math. Proc. Cambridge Philos. Soc. 99 (1986), 457-472. | MR 830359 | Zbl 0619.14004

[11] V.A. Iskovskikh, 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] Y. Kawamata, Elementary contractions of algebraic 3-folds, Ann. of Math. 119 (1984), 95-110. | MR 736561 | Zbl 0542.14007

[13] Y. Kawamata, The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603-633. | MR 744865 | Zbl 0544.14009

[14] Y. Kawamata, 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] Y. Kawamata, Small contractions of four dimensional algebraic manifolds, Math. Ann. 284 (1989), 595-600. | MR 1006374 | Zbl 0661.14009

[16] Y. Kawamata, On the length of an extremal rational curve, Invent. Math. 105 (1991), 609-611. | MR 1117153 | Zbl 0751.14007

[17] Y. Kawamata, Semistable minimal models ofthreefolds in positive or mixed characteristic, J. Alg. Geom. 3 (1994),463-491. | MR 1269717 | Zbl 0823.14026

[18] Y. Kawamata - K. Matsuda - K. Matsuki, 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] J. Kollár, Higher direct images of dualizing sheaves I, Ann. of Math. 123 (1986), 11-42. | MR 825838 | Zbl 0598.14015

[20] J. Kollár, Higher direct images of dualizing sheaves II, Ann. of Math. 124 (1986), 171-202. | MR 847955 | Zbl 0605.14014

[21] J. Kollár, Flops, Nagoya Math. J. 113 (1989), 15-36. | MR 986434 | Zbl 0645.14004

[22] J. Kollár - Y. Miyaoka - S. Mori, Rational curves on Fano varieties, preprint (1991). | MR 1180339

[23] J. Kollár - Y. Miyaoka - S. Mori, Rationally connected varieties, J. Alg. Geom. 1 (1992), 429-448. | MR 1158625 | Zbl 0780.14026

[24] J. Kollár - Y. Miyaoka - S. Mori, Rational connectedness and boundedness of Fano manifolds, J. Differential Geom. 36 (1992), 765-779. | MR 1189503 | Zbl 0759.14032

[25] J. Kollár - S. Mori, Classification of three dimensional flips, J. Amer. Math. Soc. 5 (1992), 533-703. | MR 1149195 | Zbl 0773.14004

[26] Y. Miyaoka - S. Mori, A numerical criterion for uniruledness, Ann. of Math. 124 (1986), 65-69. | MR 847952 | Zbl 0606.14030

[27] S. Mori, Projective manifolds with ample tangent bundles, Ann. of Math. 110 (1979), 593-606. | MR 554387 | Zbl 0423.14006

[28] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982),133-176. | MR 662120 | Zbl 0557.14021

[29] S. Mori, On 3-dimensional terminal singularities, Nagoya Math. J. 98 (1985), 43-66. | MR 792770 | Zbl 0589.14005

[30] S. Mori, 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] S. Mori - S. Mukai, 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] S. Mori - S. Mukai, 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] S. Mukai, 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] N. Nakayama, 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] C. Okonek - M. Schneider - H. Spindler, Vector bundles on complex projective spaces, Progress in Math. 3, Birkhäuser, Boston, 1980. | MR 561910 | Zbl 0438.32016

[36] H. Pinkham, Factorization of birational maps in dimension 3, Proc. Sympos. Pure Math. 40 (1983), 343-371. | MR 713260 | Zbl 0544.14005

[37] M. Reid, Lines on Fano 3-folds according to Shokurov, preprint (1980).

[38] M. Reid, 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] M. Reid, Projective morphisms according to Kawamata, preprint (1983). | MR 717617

[40] V.G. Sarkisov, On conic bundle structures, Math. USSR. Izv. 20 (1983), 355-390. | MR 651652 | Zbl 0593.14034

[41] V.V. Shokurov, The existence of a straight line on Fano 3-folds, Math. USSR.-Izv. 15 (1980), 173-209. | Zbl 0444.14027

[42] V.V. Shokurov, The nonvanishing theorem, Math. USSR.-Izv. 26 (1986),591-604. | Zbl 0605.14006

[43] V.V. Shokurov, 3-fold log flips, Math. USSR.-Izv. 40 (1993), 95-202. | MR 1162635 | Zbl 0785.14023

[44] K. Takeuchi, Some birational maps of Fano 3-folds, Compositio Math. 71 (1989),265-283. | Numdam | MR 1022045 | Zbl 0712.14025

[45] J. Kollár et al.., Flips and abundance for algebraic threefolds, Astérisque vol. 211, Soc. Math. de France, 1992. | MR 1225842 | Zbl 0814.14038

[46] A. Van De Ven, On uniform vector bundles, Math. Ann. 195 (1972), 245-248. | MR 291182 | Zbl 0215.43202

[47] P.M.H. Wilson, Fano fourfolds of index greater than one, J. Reine. Angew. Math. 379 (1987), 172-181. | MR 903639 | Zbl 0611.14034

[48] J. Wi, On contraction of extremal rays of Fano manifolds, J. Reine. Angew. Math. 417 (1991), 141-157. | MR 1103910 | Zbl 0721.14023