## Ascending chain condition for log canonical thresholds and termination of log flips.(English)Zbl 1109.14018

Let $$(X,B)$$ be a $$d$$-dimensional log canonical pair such that $$K_X+B$$ is numerically equivalent to an effective divisor. In the paper under review it is shown that if the ascending chain condition for log canonical thresholds holds in dimension $$d$$, the existence of log flips holds in dimension $$d$$, and the log minimal model program for log canonical pairs with $$\mathbb{R}$$-boundaries holds in dimension $$d-1$$, then any $$K_X+B$$ sequence of flips terminates. This should be compared to the result of V. V. Shokvrov [Proc. Steklov Inst. Math. 246, 315–336 (2004; Zbl 1107.14012)] in which the condition on log canonical thresholds is replaced by the ascending chain condition and the lower semicontinuity for minimal log discrepancies.

### MSC:

 14E30 Minimal model program (Mori theory, extremal rays) 14J35 $$4$$-folds 14J40 $$n$$-folds ($$n>4$$)

### Keywords:

log canonical thresholds; termination of flips

Zbl 1107.14012
Full Text:

### References:

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