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Letters of a bi-rationalist. VII: Ordered termination. (English. Russian original) Zbl 1312.14041
Proc. Steklov Inst. Math. 264, 178-200 (2009); translation from Tr. Mat. Inst. Steklova 264, 184-208 (2009).
Summary: To construct a resulting model in the LMMP, it is sufficient to prove the existence of log flips and their termination for some sequences. We prove that the LMMP in dimension $$d - 1$$ and the termination of terminal log flips in dimension $$d$$ imply, for any log pair of dimension $$d$$, the existence of a resulting model: a strictly log minimal model or a strictly log terminal Mori log fibration, and imply the existence of log flips in dimension $$d + 1$$. As a consequence, we prove the existence of a resulting model of 4-fold log pairs, the existence of log flips in dimension 5, and Geography of log models in dimension 4.
For Part V, see [the author, ibid. 246, 315–336 (2004); translation from Tr. Mat. Inst. Steklova 246, 328-351 (2004; Zbl 1107.14012)].

##### MSC:
 1.4e+06 Rational and birational maps 1.4e+31 Minimal model program (Mori theory, extremal rays)
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##### References:
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