Geodesic
On the closed cone of curves of algebraic 3-folds
Izvestiya. Mathematics, Tome 24 (1985) no. 1, pp. 193-198 
V. V. Shokurov. On the closed cone of curves of algebraic 3-folds. Izvestiya. Mathematics, Tome 24 (1985) no. 1, pp. 193-198. http://geodesic.mathdoc.fr/item/IM2_1985_24_1_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the author establishes, under natural conditions, the local polyhedrality of the closed cone of curves of a three-dimensional algebraic variety in the part that is negative with respect to the canonical class. In particular, it is shown that there always exists an extremal ray giving a contraction. The results can be used in three-dimensional birational geometry. Bibliography: 7 titles.

[1] Kawamata Y., “A generalization of Kodaira–Ramanujam's vanishing theorem”, Math. Ann., 261 (1982), 43–46 | DOI | MR | Zbl

[2] Kawamata Y., On the finiteness of generators of a pluri-canonical ring for a 3-fold of a general type, preprint, 1983

[3] Kawamata Y., Elementary contractions of algebraic 3-folds, preprint, 1983 | MR

[4] Mori S., “Threefolds whose canonical bundles are not numerically effective”, Ann. of Math., 116 (1982), 133–176 | DOI | MR | Zbl

[5] Ried M., “Canonical 3-folds”, Algebraic Geometry, Angers, 1979, 273–310 | MR

[6] Shokurov V. V., “Ekstremalnye styagivaniya trekhmernykh algebraicheskikh mnogoobrazii”, Konstruktivnaya algebraicheskaya geometriya, Mezhvuzovskii sbornik statei, Yaroslavl, 1984

[7] Ried M., Projective morphisms according to Kawamata, preprint, 1983 | MR