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Algebraic 3-folds and the diagram method. (English. Russian original) Zbl 0731.14024
Math. USSR, Izv. 37, No. 1, 157-189 (1991); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 54, No. 4, 810-845 (1990).
This paper is devoted to the application of the diagram method to the study of projective threefolds with log-terminal singularities. The idea of the diagram method is contained in the observation that the negative part of Mori’s polyhedron forms a special system of roots; the geometry and the combinatorics of this root system provides a lot of information about the geometry of the threefold. This method has been initially applied by the author and V. Alexeev to the study of the log-terminal Del Pezzo surfaces.
Reviewer: A.Iliev (Sofia)

MSC:
14J30 \(3\)-folds
14E30 Minimal model program (Mori theory, extremal rays)
14B05 Singularities in algebraic geometry
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