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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V. V. Shokurov (1986) studied this question.
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