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Mld’s vs thresholds and flips. (English) Zbl 1194.14020

The authors prove that the Log Minimal Model Program, the ascending chain condition conjecture for minimal log discrepancies and the boundedness of canonical Mori-Fano varieties in every dimension up to \(n\) imply the following: the ascending chain condition conjecture a-log canonical thresholds (natural generalization of standard log canonical thresholds) in every dimension up to \(n\), the ascending chain condition conjecture for standard log canonical thresholds in every dimension up to \(n+1\), the termination of log flips for effective log canonical log pairs in every dimension up to \(n+1\).

MSC:

14E30 Minimal model program (Mori theory, extremal rays)

Citations:

Zbl 1107.14012
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References:

[1] DOI: 10.1215/S0012-7094-93-06922-0 · Zbl 0791.14006
[2] DOI: 10.1142/S0129167X94000395 · Zbl 0838.14028
[3] Ambro F., Math. Res. Lett. 6 pp 5– (1999)
[4] Ambro F., Central Europ. Math. J. 4 (2) pp 1– (2006)
[5] DOI: 10.1215/S0012-7094-07-13615-9 · Zbl 1109.14018
[6] DOI: 10.1007/BF02678179 · Zbl 0873.14003
[7] Cheltsov I., Math. Sb. 193 pp 5– (2002)
[8] Corti A., J. Alg. Geom. 4 pp 223– (1994)
[9] DOI: 10.1070/RM2005v060n01ABEH000807 · Zbl 1079.14023
[10] Kawamata Y., Internat. J. Math. 3 pp 5– (1992)
[11] DOI: 10.1007/BF01445123 · Zbl 0818.14002
[12] Kollár J., Astérisque 211 pp 155– (1992)
[13] Kollár J., J. Di{\currency}. Geom. 36 pp 3– (1992)
[14] DOI: 10.3792/pjaa.76.73 · Zbl 0981.14016
[15] Kernan J., Manuscr. Math. 114 pp 3– (2004)
[16] Prokhorov Yu., J. Alg. Geom. 18 pp 151– (2009)
[17] DOI: 10.1070/IM1993v040n01ABEH001862 · Zbl 0785.14023
[18] DOI: 10.1007/BF02362335 · Zbl 0873.14014
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