Minimal models of algebraic threefolds : Mori's program
Séminaire Bourbaki : volume 1988/89, exposés 700-714, Astérisque, no. 177-178 (1989), Exposé no. 712, 24 p.
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     author = {Koll\'ar, J\'anos},
     title = {Minimal models of algebraic threefolds : {Mori's} program},
     booktitle = {S\'eminaire Bourbaki : volume 1988/89, expos\'es 700-714},
     series = {Ast\'erisque},
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     publisher = {Soci\'et\'e math\'ematique de France},
     number = {177-178},
     year = {1989},
     mrnumber = {1040578},
     zbl = {0711.14008},
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     url = {http://www.numdam.org/item/SB_1988-1989__31__303_0/}
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Kollár, János. Minimal models of algebraic threefolds : Mori's program, dans Séminaire Bourbaki : volume 1988/89, exposés 700-714, Astérisque, no. 177-178 (1989), Exposé no. 712, 24 p. http://www.numdam.org/item/SB_1988-1989__31__303_0/

H. Clemens, J. Kollár and S. Mori, "Higher Dimensional Complex Geometry," Asterisque 166, 1988 This booklet contains the simplest known proofs of (2.9) and (4.10). It also contains a lot of background material.. | MR | Zbl

Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the Minimal Model Problem, in "Algebraic Geometry, Sendai," Adv. Stud. Pure Math. vol 10. T. Oda ed., Kinokuniya - North-Holland, 1987, pp. 283-360. The most complete discussion of (2.9) and related questions. | MR | Zbl

J. Kollár, The structure of algebraic threefolds - an introduction to Mori's program, Bull. AMS 17 (1987), 211-273. A leisurely introduction, aimed at all mathematicians. | MR | Zbl

M. Reid, Young person's guide to canonical singularities, in "Algebraic Geometry Bowdoin 1985," Proc. Symp. Pure Math. vol. 46, 1987, pp. 345-416. A nice treatment of the relevant singularities. | MR | Zbl

P. M. H. Wilson, Toward a birational classification of algebraic varieties, Bull. London Math. Soc. 19 (1987), 1-48. An overview aimed at algebraic geometers, written before [Mo4] appeared. | MR | Zbl

[B] X. Benveniste, Sur l'anneau canonique de certaines variétés de dimension 3, Inv. Math. 73 (1983), 157-164. | MR | Zbl

[D] V. I. Danilov, The geometry of toric varieties, Russian Math. Surveys 33 (1978), 97-154. | MR | Zbl

[F] T. Fujita, Zariski decomposition and canonical rings of elliptic threefolds, J. Math. Soc. Japan 38 (1986), 19-37. | MR | Zbl

[Ka1] Y. Kawamata, On the finiteness of generators of the pluri-canonical ring for a threefold of general type, Amer. J. Math. 106 (1984), 1503-1512. | MR | Zbl

[Ka2] Y. Kawamata, The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603-633. | MR | Zbl

[Ka3] Y. Kawamata, The crepant blowing-up of 3-dimensional canonical singularities and its application to the degeneration of surfaces, Ann. of Math 127 (1988), 93-163. | MR | Zbl

[Ko1] J. Kollár, The Cone Theorem, Ann. of Math. 120 (1984), 1-5. | MR | Zbl

[KM] J. Kollár and S. Mori, soon to be written up.

[KSB] J. Kollár and N. Shepherd-Barron, Threefolds and deformations of surface singularities, Inv. Math. 91 (1988), 299-338. | MR | Zbl

[Mi] Y. Miyaoka, On the Kodaira dimension of minimal threefolds, Math. Ann. 281 (1988), 325-332. | MR | Zbl

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

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

[Mo2] S. Mori, On 3-dimensional terminal singularities, Nagoya Math. J. 98 (1985), 43-66. | MR | Zbl

[Mo3] S. Mori, Minimal models for semistable degenerations of surfaces, Lectures at Columbia University (1985), unpublished.

[Mo4] S. Mori, Flip theorem and the existence of minimal models for 3-folds, Journal AMS 1 (1988), 117-253. | MR | Zbl

[MS] D. Morrison and G. Stevens, Terminal quotient singularities in dimension three and four, Proc. AMS 90 (1984), 15-20. | MR | Zbl

[P] T. Peternell, Rational curves on Moishezon threefolds, in "Complex Analysis and Algebraic Geometry," Springer LN. 1194, 1986, pp. 133-144. | MR | Zbl

[R1] M. Reid, Canonical Threefolds, in "Géometrie Algébrique Angers," A. Beauville ed., Sijthoff & Noordhoff, 1980, pp. 273-310. | MR | Zbl

[R2] M. Reid, Projective morphisms according to Kawamata, preprint, Univ. of Warwick (1983). | MR

[R3] M. Reid, Minimal models of canonical threefolds, in "Algebraic Varieties and Analytic Varieties," Adv. Stud. Pure Math. vol 1. S. Iitaka ed., Kinokuniya and North-Holland, 1983, pp. 131-180. | MR | Zbl

[S1] V. V. Shokurov, letter to M. Reid (1985).

[S2] V. V. Shokurov, Theorem on nonvanishing, Math. USSR Izv. 26 (1986), 591-604. | Zbl

[T] S. Tsunoda, Degenerations of Surfaces, in "Algebraic Geometry, Sendai," Adv. Stud. Pure Math. vol 10. T. Oda ed., Kinokuniya - North-Holland, 1987, pp. 755-764. | MR | Zbl