2019 Fiscal Year Final Research Report
On resolution of singularities of algebraic varieties in positive characteristic
| Project/Area Number |
16K05100
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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 | Chubu University (2019)
Kyoto University (2016-2018) |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | 代数幾何学 / 特異点解消 / IFP |
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| Outline of Final Research Achievements |
The target of this research project is the problem of resolution of singularities. The problem of resolution of singularities is one of the most important problem in algebraic geometry. It is established in characteristic 0, in any dimension, due to Professor Heisuke Hironaka. However, it is still widely open in positive characteristic. we introduced the new approach, called IFP, to solve this important problem. I have developed IFP with the coworker Kenji Matsuki, a professor in Purdue university. During the period of this research project, we established two new proof for the resolution of singularities for surfaces, from the view point of IFP. We also have some new input for 3-fold case, though which is still work in progress.
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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 |
この研究では本研究者が提案し推進しているIFPというアプローチを用いて曲面の特異点解消について新しい証明を与えた. この結果は2通りの意義がある. 一つは, これが不変量の減少を見ることで特異点解消を確立する構成的な証明である点である．曲面の特異点解消の構成的な証明はこれまで知られていなかった. もう一つの意義は, 一般次元の特異点解消の為のプログラムであるIFPの有効性を示したという点である.
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