| Budget Amount *help |
¥10,660,000 (Direct Cost: ¥8,200,000、Indirect Cost: ¥2,460,000)
Fiscal Year 2015: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2014: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2012: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
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| Outline of Final Research Achievements |
I studied the ACC for minimal log discrepancies, using generic limits introduced by de Fernex, Mustata and Kollar. I proved the discreteness of log discrepancies over all log canonical pairs for a fixed variety and fixed exponents, and obtained the ACC for minimal log discrepancies on local complete intersection singularities. Even when the exponents are not fixed, I proved the ACC for minimal log discrepancies greater than 1 on smooth 3-folds. Also, I showed the ideal-adic semi-continuity of minimal log discrepancies on surfaces.
As a boundedness problem of singularities, I proved that the index of a 3-fold strictly canonical singularity is at most 6.
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