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.
@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},
     mrnumber = {1475773},
     zbl = {0908.14002},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1997_4_24_1_63_0/}
}
TY  - JOUR
AU  - Kachi, Yasuyuki
TI  - Extremal contractions from $4$-dimensional manifolds to $3$-folds
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1997
SP  - 63
EP  - 131
VL  - 24
IS  - 1
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1997_4_24_1_63_0/
LA  - en
ID  - ASNSP_1997_4_24_1_63_0
ER  - 
%0 Journal Article
%A Kachi, Yasuyuki
%T Extremal contractions from $4$-dimensional manifolds to $3$-folds
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1997
%P 63-131
%V 24
%N 1
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_1997_4_24_1_63_0/
%G en
%F 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://archive.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 | Zbl

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

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

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

[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 | Zbl

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

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

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

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

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

[11] V.A. Iskovskikh, Double projection from a line on Fano threefolds of the first kind, Math. USSR.-Sb. 66 (1990), 265-284. | MR | Zbl

[12] Y. Kawamata, Elementary contractions of algebraic 3-folds, Ann. of Math. 119 (1984), 95-110. | MR | Zbl

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

[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 | Zbl

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

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

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

[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 | Zbl

[19] J. Kollár, Higher direct images of dualizing sheaves I, Ann. of Math. 123 (1986), 11-42. | MR | Zbl

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

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

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

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

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

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

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

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

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

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

[30] S. Mori, Flip theorem and the existence of minimal models for 3-folds, J. Amer. Math. Soc. 1 (1988), 117-253. | MR | Zbl

[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

[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

[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 | Zbl

[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 | Zbl

[35] C. Okonek - M. Schneider - H. Spindler, Vector bundles on complex projective spaces, Progress in Math. 3, Birkhäuser, Boston, 1980. | MR | Zbl

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

[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 | Zbl

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

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

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

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

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

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

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

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

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

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