| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
I proved that the minimal log discrepancy on a smooth surface is computed by the divisor obtained by a weighted blow-up. I solved negatively the question of whether a divisor computing the minimal log discrepancy computes a log canonical threshold, by providing a counter-example on a smooth surface.
I reduced the ascending chain condition (ACC) for minimal log discrepancies on a smooth threefold to the case when the boundary is decomposed into a canonical part and the maximal ideal to some power. Moreover, I proved the boundedness of a divisor computing the minimal log discrepancy when the log canonical threshold of the maximal ideal is either at most one-half or at least one. In particular, I obtained the ACC at minimal log discrepancy one.
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