2023 Fiscal Year Final Research Report
Singularities in the log minimal model program
| Project/Area Number |
19K03423
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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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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2024-03-31
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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 / 因子収縮写像 |
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| Outline of Final Research Achievements |
I established the ascending chain condition (ACC) for minimal log discrepancies on smooth threefolds completely. It implies, on smooth threefolds, the ACC for a-lc thresholds, the uniform ideal-adic semi-continuity and Nakamura's boundedness, which means the boundedness of the log discrepancy of some divisor that computes the minimal log discrepancy. The results are extended to the statements on a fixed terminal quotient threefold singularity.
From the point of view of the ACC problem, I studied threefold log divisorial contractions from a canonical threefold to a canonical singularity of semistable type.
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| Free Research Field |
代数幾何学
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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．対数的極小モデルプログラムと呼ばれる理論によって代数多様体を分類するとき，代数多様体の特異点を制御する必要が生じます．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．特に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完全に解決しました．
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