@incollection{SB_1988-1989__31__303_0, 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}, note = {talk:712}, pages = {303--326}, publisher = {Soci\'et\'e math\'ematique de France}, number = {177-178}, year = {1989}, mrnumber = {1040578}, zbl = {0711.14008}, language = {en}, url = {http://www.numdam.org/item/SB_1988-1989__31__303_0/} }

TY - CHAP AU - Kollár, János TI - Minimal models of algebraic threefolds : Mori's program BT - Séminaire Bourbaki : volume 1988/89, exposés 700-714 AU - Collectif T3 - Astérisque N1 - talk:712 PY - 1989 SP - 303 EP - 326 IS - 177-178 PB - Société mathématique de France UR - http://www.numdam.org/item/SB_1988-1989__31__303_0/ LA - en ID - SB_1988-1989__31__303_0 ER -

%0 Book Section %A Kollár, János %T Minimal models of algebraic threefolds : Mori's program %B Séminaire Bourbaki : volume 1988/89, exposés 700-714 %A Collectif %S Astérisque %Z talk:712 %D 1989 %P 303-326 %N 177-178 %I Société mathématique de France %U http://www.numdam.org/item/SB_1988-1989__31__303_0/ %G en %F SB_1988-1989__31__303_0

Kollár, János. Minimal models of algebraic threefolds : Mori's program, inSéminaire Bourbaki : volume 1988/89, exposés 700-714, Astérisque, no. 177-178 (1989), Talk no. 712, 24 p. http://www.numdam.org/item/SB_1988-1989__31__303_0/

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

, and , "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

, and ,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

,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

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

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

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

,[Ka1] 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] The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603-633. | MR | Zbl

,[Ka3] 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] The Cone Theorem, Ann. of Math. 120 (1984), 1-5. | MR | Zbl

,[KM]

and , soon to be written up.[KSB] Threefolds and deformations of surface singularities, Inv. Math. 91 (1988), 299-338. | MR | Zbl

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

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

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

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

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

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

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

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

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

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

,[R3] 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] letter to M. Reid (1985).

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

,[T] 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

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