Singularities in the minimal model program
| Project/Area Number |
16K05099
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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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) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| 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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| Keywords | 極小対数的食違い係数 / 昇鎖律 / 標準特異点 / 重み付き爆発 / 代数学 / 代数幾何学 |
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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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| Academic Significance and Societal Importance of the Research Achievements |
代数多様体とは，連立多項式の共通零点集合として定義される図形です．高次元の代数多様体の分類においては，特異点の制御が欠かせません．私は極小対数的食違い係数と呼ばれる特異点の不変量を研究しました．いったい何がその不変量を決定するのか，よく分かっていませんでしたが，私は2次元の場合に満足のいく結果を得ました．また，極小対数的食違い係数の重要な予想である昇鎖律予想を，なめらかな3次元代数多様体上で考察しました．
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Report
(4 results)
Research Products
(6 results)
