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Log minimal models according to Shokurov. (English) Zbl 1194.14021
The author proves that termination of terminal flips in dimension $$d$$ implies that any klt log pair of dimension $$d$$ is either birational to its log minimal model or to a Mori fibre space. This important result implies, in particular, that any klt log pair of dimension $$4$$ is either birational to its log minimal model or to a Mori fibre space. The paper is very nicely written.

##### MSC:
 1.4e+31 Minimal model program (Mori theory, extremal rays)
##### Keywords:
log minimal model; termination of log flips
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