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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 (\(n>4\))

Citations:

Zbl 1107.14012
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References:

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