Kollár, János
Minimal models of algebraic threefolds : Mori's program
Séminaire Bourbaki, Tome 31 (1988-1989) , Exposé no. 712 , p. 303-326
Zbl 0711.14008 | MR 1040578
URL stable : http://www.numdam.org/item?id=SB_1988-1989__31__303_0

Bibliographie

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 1004926 | Zbl 0689.14016

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 946243 | Zbl 0672.14006

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 903730 | Zbl 0649.14022

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 927963 | Zbl 0634.14003

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 865038 | Zbl 0612.14033

[B] X. Benveniste, Sur l'anneau canonique de certaines variétés de dimension 3, Inv. Math. 73 (1983), 157-164. MR 707354 | Zbl 0539.14025

[D] V.I. Danilov, The geometry of toric varieties, Russian Math. Surveys 33 (1978), 97-154. MR 495499 | Zbl 0425.14013

[F] T. Fujita, Zariski decomposition and canonical rings of elliptic threefolds, J. Math. Soc. Japan 38 (1986), 19-37. MR 816221 | Zbl 0627.14031

[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 765589 | Zbl 0587.14027

[Ka2] Y. Kawamata, The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603-633. MR 744865 | Zbl 0544.14009

[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 924674 | Zbl 0651.14005

[Ko1] J. Kollár, The Cone Theorem, Ann. of Math. 120 (1984), 1-5. MR 750714 | Zbl 0544.14010

[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 922803 | Zbl 0642.14008

[Mi] Y. Miyaoka, On the Kodaira dimension of minimal threefolds, Math. Ann. 281 (1988), 325-332. MR 949837 | Zbl 0625.14023

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

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

[Mo2] S. Mori, On 3-dimensional terminal singularities, Nagoya Math. J. 98 (1985), 43-66. MR 792770 | Zbl 0589.14005

[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 924704 | Zbl 0649.14023

[MS] D. Morrison and G. Stevens, Terminal quotient singularities in dimension three and four, Proc. AMS 90 (1984), 15-20. MR 722406 | Zbl 0536.14003

[P] T. Peternell, Rational curves on Moishezon threefolds, in "Complex Analysis and Algebraic Geometry," Springer LN. 1194, 1986, pp. 133-144. MR 855881 | Zbl 0602.14039

[R1] M. Reid, Canonical Threefolds, in "Géometrie Algébrique Angers," A. Beauville ed., Sijthoff & Noordhoff, 1980, pp. 273-310. MR 605348 | Zbl 0451.14014

[R2] M. Reid, Projective morphisms according to Kawamata, preprint, Univ. of Warwick (1983). MR 717617

[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 715649 | Zbl 0558.14028

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

[S2] V.V. Shokurov, Theorem on nonvanishing, Math. USSR Izv. 26 (1986), 591-604. Zbl 0605.14006

[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 946256 | Zbl 0682.14007