By Shokurov V. V.
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120, 1-5 (1984). J. 14. Kolls and S. Mort, Classification of Three-Dimensional Flips, preprint. 15. J. , "Flips and abundance for algebraic threefolds," A Summer Seminar at the University of Utah, Salt Lake City, 1991, Asterisque, 211 (1992). 16. T. Luo, On the Divisorial Eztremal Contractions of Threefolds: Divisor to a Point, preprint. 17. Y. Miyaoka, "Abundance conjecture for 3-folds: v = 1 case," Comp. , 68, 203-220 (1988). 18. V. V. Nikulin, Diagram Method for 3-Folds and Its Application to KShler Cone and Picard Number of Calabi-Yau 3-Folds.
2698 24. V. V. Shokurov, "Problems about Fano varieties," In: Birational Geomet~ of Algebraic Varieties: Open problema. The XXIIIrd International Symposium, Division of Mathematica, The Taniguehi Foundation. Aug. ~-27, 1988, pp. 30-32. 25. V. V. Shokurov, Special 3-Dimensional Flips, preprint, MPI/89-22. 26. V. V. Shokurov, "3-Fold log flips," Izv. Akad. IVauk SSSR. Ser. , 56, No. 1,105-201 (1992). 27. V. V. Shokurov, "Anticanonical boundedness for curves," Appendix to . 28. V. V. Shokurov, "Semi-stable 3-fold flips," Izv.
22. C o r o l l a r y . By elementary flops we mean blow-ups and blow-downs X --+ Y / S with relative Picaxd number 1, being numerically trivial with respect to the log divisor K x + B x , but not the usual flops. The latter axe decomposable into two elementary small flops. Flops are directed with respect to some divisor. 1. P r o b l e m . Of course in dimension 2, we can prove the theorem for all weakly log canonical models and their flops. However, it appears that projectivity is very important for dimension 3 and higher.