Study of singularities in the minimal model theory in higher dimension
| Project/Area Number |
20684002
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000)
Fiscal Year 2011: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2010: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2009: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2008: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
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| Keywords | 極小モデル理論 / 極小対数的食違い係数 / モチーフ積分 / イデアル進位相 / 昇鎖律 / 対数的標準特異点 / Riemann-Roch公式 / 因子収縮写像 / 特異点 |
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| Research Abstract |
I reduced the boundedness of minimal log discrepancies to the boundedness of multiplicities or embedding dimensions by using Riemann-Roch theorem, and through the analysis of Artinian rings as hyperplane sections, I recovered this boundedness in dimension 3 and the characterisation of 3-fold Gorenstein terminal singularities. From the point of view of the ascending chain condition, I studied the extension of the ideal-adic semi-continuity of log canonical thresholds due to Kollar and de Fernex, Ein, Mustata, to minimal log discrepancies, and proved this semi-continuity in the setting of purely log terminal singularities by using the theory of motivic integration. I studied also the classification of 3-fold divisorial contractions.
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Report
(6 results)
Research Products
(44 results)
