@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://www.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://www.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://www.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, Série 4, Tome 24 (1997) no. 1, pp. 63-131. http://www.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 | Zbl
,[2] A note on nonvanishing and applications, Duke Math. J. 72 (1993), 739-755. | MR | Zbl
- ,[3] On good contractions of smooth varieties, preprint (1996). | MR
- ,[4] Variétés de Prym et Jacobiennes intermédiaires, Ann. Sci. École Norm. Sup. 10 (1977), 309-391. | Numdam | MR | Zbl
,[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 | Zbl
,[6] Connexité rationnelle des variété de Fano, Ann. Sci. École Norm. Sup. 25 (1992), 539-545. | Numdam | MR | Zbl
,[7] Decomposition of certain birational morphisms, Math. USSR.-Izv. 16 (1981), 419-429. | Zbl
,[8] On Del Pezzofibrations over curves, Osaka Math. J. 27 (1990), 229-245. | MR | Zbl
,[9] Vektorbündel vom rang 2 über dem n-dimensionalen komplex-projektiven raum, Manuscripta. Math. 16 (1975), 75-100. | MR | Zbl
- ,[10] Generalized adjunction and applications, Math. Proc. Cambridge Philos. Soc. 99 (1986), 457-472. | MR | Zbl
,[11] Double projection from a line on Fano threefolds of the first kind, Math. USSR.-Sb. 66 (1990), 265-284. | MR | Zbl
,[12] Elementary contractions of algebraic 3-folds, Ann. of Math. 119 (1984), 95-110. | MR | Zbl
,[13] The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603-633. | MR | Zbl
,[14] 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] Small contractions of four dimensional algebraic manifolds, Math. Ann. 284 (1989), 595-600. | MR | Zbl
,[16] On the length of an extremal rational curve, Invent. Math. 105 (1991), 609-611. | MR | Zbl
,[17] Semistable minimal models ofthreefolds in positive or mixed characteristic, J. Alg. Geom. 3 (1994),463-491. | MR | Zbl
,[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 | Zbl
- - ,[19] Higher direct images of dualizing sheaves I, Ann. of Math. 123 (1986), 11-42. | MR | Zbl
,[20] Higher direct images of dualizing sheaves II, Ann. of Math. 124 (1986), 171-202. | MR | Zbl
,[21] Flops, Nagoya Math. J. 113 (1989), 15-36. | MR | Zbl
,[22] Rational curves on Fano varieties, preprint (1991). | MR
- - ,[23] Rationally connected varieties, J. Alg. Geom. 1 (1992), 429-448. | MR | Zbl
- - ,[24] Rational connectedness and boundedness of Fano manifolds, J. Differential Geom. 36 (1992), 765-779. | MR | Zbl
- - ,[25] Classification of three dimensional flips, J. Amer. Math. Soc. 5 (1992), 533-703. | MR | Zbl
- ,[26] A numerical criterion for uniruledness, Ann. of Math. 124 (1986), 65-69. | MR | Zbl
- ,[27] Projective manifolds with ample tangent bundles, Ann. of Math. 110 (1979), 593-606. | MR | Zbl
,[28] Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982),133-176. | MR | Zbl
,[29] On 3-dimensional terminal singularities, Nagoya Math. J. 98 (1985), 43-66. | MR | Zbl
,[30] Flip theorem and the existence of minimal models for 3-folds, J. Amer. Math. Soc. 1 (1988), 117-253. | MR | Zbl
,[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
- ,[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
- ,[33] Biregular classification of Fano 3-folds and Fano manifolds of coindex 3, Proc. Nat. Acad. Sci. USA 86 (1989), 3000-3002. | MR | Zbl
,[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 | Zbl
,[35] Vector bundles on complex projective spaces, Progress in Math. 3, Birkhäuser, Boston, 1980. | MR | Zbl
- - ,[36] Factorization of birational maps in dimension 3, Proc. Sympos. Pure Math. 40 (1983), 343-371. | MR | Zbl
,[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 | Zbl
,[39] Projective morphisms according to Kawamata, preprint (1983). | MR
,[40] On conic bundle structures, Math. USSR. Izv. 20 (1983), 355-390. | MR | Zbl
,[41] The existence of a straight line on Fano 3-folds, Math. USSR.-Izv. 15 (1980), 173-209. | Zbl
,[42] The nonvanishing theorem, Math. USSR.-Izv. 26 (1986),591-604. | Zbl
,[43] 3-fold log flips, Math. USSR.-Izv. 40 (1993), 95-202. | MR | Zbl
,[44] Some birational maps of Fano 3-folds, Compositio Math. 71 (1989),265-283. | Numdam | MR | Zbl
,[45] Flips and abundance for algebraic threefolds, Astérisque vol. 211, Soc. Math. de France, 1992. | MR | Zbl
et al..,[46] On uniform vector bundles, Math. Ann. 195 (1972), 245-248. | MR | Zbl
,[47] Fano fourfolds of index greater than one, J. Reine. Angew. Math. 379 (1987), 172-181. | MR | Zbl
,[48] On contraction of extremal rays of Fano manifolds, J. Reine. Angew. Math. 417 (1991), 141-157. | MR | Zbl
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