On minimal log discrepancies on varieties with fixed Gorenstein index

Abstract

We generalize the rationality theorem of the accumulation points of log canonical thresholds which was proved by Hacon, M\textsuperscript{c}Kernan, and Xu. Further, we apply the rationality to the ACC problem on the minimal log discrepancies. We study the set of log discrepancies on varieties with fixed Gorenstein index. As a corollary, we prove that the minimal log discrepancies of three-dimensional canonical pairs with fixed coefficients satisfy the ACC.

21 pages

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• An optimal gap of minimal log discrepancies of threefold non-canonical singularities
• Uniform rational polytopes of foliated threefolds and the global ACC
• On termination of flips and exceptionally non-canonical singularities
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• Rational nef and anti-nef polytopes are not uniform
• Infinitesimal structure of log canonical thresholds