Extremal contractions from 4-dimensional manifolds to 3-folds

 Access to full text

 Full (PDF)

1. [1] T. Ando, On extremal rays of the higher dimensional varieties, Invent. Math.81 (1985), 347-357. Zbl0554.14001MR799271
2. [2] M. Andreatta - J. Wi, A note on nonvanishing and applications, Duke Math. J.72 (1993), 739-755. Zbl0853.14003MR1253623
3. [3] M. Andreatta - J. Wi, On good contractions of smooth varieties, preprint (1996). MR1620110
4. [4] A. Beauville, Variétés de Prym et Jacobiennes intermédiaires, Ann. Sci. École Norm. Sup.10 (1977), 309-391. Zbl0368.14018MR472843
5. [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. Zbl0633.14021MR916706
6. [6] F. Campana, Connexité rationnelle des variété de Fano, Ann. Sci. École Norm. Sup.25 (1992), 539-545. Zbl0783.14022MR1191735
7. [7] V.I. Danilov, Decomposition of certain birational morphisms, Math. USSR.-Izv. 16 (1981), 419-429. Zbl0464.14003
8. [8] T. Fujita, On Del Pezzofibrations over curves, Osaka Math. J.27 (1990), 229-245. Zbl0715.14030MR1066621
9. [9] H. Grauert - G. Mülich, Vektorbündel vom rang 2 über dem n-dimensionalen komplex-projektiven raum, Manuscripta. Math. 16 (1975), 75-100. Zbl0318.32027MR382278
10. [10] P. Ionescu, Generalized adjunction and applications, Math. Proc. Cambridge Philos. Soc. 99 (1986), 457-472. Zbl0619.14004MR830359
11. [11] V.A. Iskovskikh, Double projection from a line on Fano threefolds of the first kind, Math. USSR.-Sb. 66 (1990), 265-284. Zbl0691.14027MR993458
12. [12] Y. Kawamata, Elementary contractions of algebraic 3-folds, Ann. of Math. 119 (1984), 95-110. Zbl0542.14007MR736561
13. [13] Y. Kawamata, The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603-633. Zbl0544.14009MR744865
14. [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. Zbl0651.14005MR924674
15. [15] Y. Kawamata, Small contractions of four dimensional algebraic manifolds, Math. Ann. 284 (1989), 595-600. Zbl0661.14009MR1006374
16. [16] Y. Kawamata, On the length of an extremal rational curve, Invent. Math. 105 (1991), 609-611. Zbl0751.14007MR1117153
17. [17] Y. Kawamata, Semistable minimal models ofthreefolds in positive or mixed characteristic, J. Alg. Geom.3 (1994),463-491. Zbl0823.14026MR1269717
18. [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. Zbl0672.14006MR946243
19. [19] J. Kollár, Higher direct images of dualizing sheaves I, Ann. of Math. 123 (1986), 11-42. Zbl0598.14015MR825838
20. [20] J. Kollár, Higher direct images of dualizing sheaves II, Ann. of Math. 124 (1986), 171-202. Zbl0605.14014MR847955
21. [21] J. Kollár, Flops, Nagoya Math. J.113 (1989), 15-36. Zbl0645.14004MR986434
22. [22] J. Kollár - Y. Miyaoka - S. Mori, Rational curves on Fano varieties, preprint (1991). Zbl0776.14012MR1180339
23. [23] J. Kollár - Y. Miyaoka - S. Mori, Rationally connected varieties, J. Alg. Geom.1 (1992), 429-448. Zbl0780.14026MR1158625
24. [24] J. Kollár - Y. Miyaoka - S. Mori, Rational connectedness and boundedness of Fano manifolds, J. Differential Geom.36 (1992), 765-779. Zbl0759.14032MR1189503
25. [25] J. Kollár - S. Mori, Classification of three dimensional flips, J. Amer. Math. Soc.5 (1992), 533-703. Zbl0773.14004MR1149195
26. [26] Y. Miyaoka - S. Mori, A numerical criterion for uniruledness, Ann. of Math.124 (1986), 65-69. Zbl0606.14030MR847952
27. [27] S. Mori, Projective manifolds with ample tangent bundles, Ann. of Math.110 (1979), 593-606. Zbl0423.14006MR554387
28. [28] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math.116 (1982),133-176. Zbl0557.14021MR662120
29. [29] S. Mori, On 3-dimensional terminal singularities, Nagoya Math. J.98 (1985), 43-66. Zbl0589.14005MR792770
30. [30] S. Mori, Flip theorem and the existence of minimal models for 3-folds, J. Amer. Math. Soc.1 (1988), 117-253. Zbl0649.14023MR924704
31. [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. Zbl0537.14026
32. [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. Zbl0800.14021
33. [33] S. Mukai, Biregular classification of Fano 3-folds and Fano manifolds of coindex 3, Proc. Nat. Acad. Sci. USA86 (1989), 3000-3002. Zbl0679.14020MR995400
34. [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. Zbl0649.14003MR946250
35. [35] C. Okonek - M. Schneider - H. Spindler, Vector bundles on complex projective spaces, Progress in Math.3, Birkhäuser, Boston, 1980. Zbl0438.32016MR561910
36. [36] H. Pinkham, Factorization of birational maps in dimension 3, Proc. Sympos. Pure Math.40 (1983), 343-371. Zbl0544.14005MR713260
37. [37] M. Reid, Lines on Fano 3-folds according to Shokurov, preprint (1980). 
38. [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. Zbl0558.14028MR715649
39. [39] M. Reid, Projective morphisms according to Kawamata, preprint (1983). MR717617
40. [40] V.G. Sarkisov, On conic bundle structures, Math. USSR. Izv. 20 (1983), 355-390. Zbl0593.14034MR651652
41. [41] V.V. Shokurov, The existence of a straight line on Fano 3-folds, Math. USSR.-Izv. 15 (1980), 173-209. Zbl0444.14027
42. [42] V.V. Shokurov, The nonvanishing theorem, Math. USSR.-Izv. 26 (1986),591-604. Zbl0605.14006
43. [43] V.V. Shokurov, 3-fold log flips, Math. USSR.-Izv.40 (1993), 95-202. Zbl0785.14023MR1162635
44. [44] K. Takeuchi, Some birational maps of Fano 3-folds, Compositio Math. 71 (1989),265-283. Zbl0712.14025MR1022045
45. [45] J. Kollár et al.., Flips and abundance for algebraic threefolds, Astérisque vol. 211, Soc. Math. de France, 1992. Zbl0814.14038MR1225842
46. [46] A. Van De Ven, On uniform vector bundles, Math. Ann.195 (1972), 245-248. Zbl0215.43202MR291182
47. [47] P.M.H. Wilson, Fano fourfolds of index greater than one, J. Reine. Angew. Math.379 (1987), 172-181. Zbl0611.14034MR903639
48. [48] J. Wi, On contraction of extremal rays of Fano manifolds, J. Reine. Angew. Math.417 (1991), 141-157. Zbl0721.14023MR1103910

1. Massimiliano Mella, On del Pezzo fibrations