Geodesic
The nonvanishing theorem
Izvestiya. Mathematics, Tome 26 (1986) no. 3, pp. 591-604 
V. V. Shokurov. The nonvanishing theorem. Izvestiya. Mathematics, Tome 26 (1986) no. 3, pp. 591-604. http://geodesic.mathdoc.fr/item/IM2_1986_26_3_a5/
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     author = {V. V. Shokurov},
     title = {The nonvanishing theorem},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_26_3_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The main result of the paper is a nonvanishing theorem that is a sufficient condition for nontriviality of the zeroth cohomology group of inverse sheaves. In addition, applications of this theorem to multidimensional projective geometry are indicated and problems illuminating further insight into the theory of Mori extremal rays are formulated. Bibliography: 14 titles.

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[8] Ried M., Projective morphisms according to Kawamata, preprint Math. Inst. Univ. of Warwick, 1983

[9] Shokurov V. V., “O zamknutom konuse krivykh trekhmernykh algebraicheskikh mnogoobrazii”, Izv. AN SSSR. Ser. matem., 48:1 (1984), 203–208 | MR

[10] Shokurov V. V., “Ekstremalnye styagivaniya trekhmernykh algebraicheskikh mnogoobrazii”, Biratsionalnaya geometriya algebraicheskikh mnogoobrazii, Yaroslavl, 1983, 74–90 | MR | Zbl

[11] Shokurov V. V., “Ekstremalnye morfizmy trekhmernykh algebraicheskikh mnogoobrazii”, Tezisy XV Vsesoyuznoi algebraicheskoi konferentsii, Minsk, 1983, 224

[12] Viehweg E., “Vanishing theorems”, J. reine u. angew. Math., 335 (1982), 1–8 | MR | Zbl

[13] Kawamata Y., “The cone of curves of algebraic varieties”, Ann. of Math., 119 (1984), 603–633 | DOI | MR | Zbl

[14] Kollar J., “The cone theorem: Note to a paper by Y. Kawamata, The cone of curves of algebraic varieties”, Ann. of Math., 120 (1984), 1–5 | DOI | MR | Zbl