2021 Fiscal Year Final Research Report
Topological types and analytic invariants of complex surface singularities
| Project/Area Number |
17K05216
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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 |
Geometry
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| Research Institution | Yamagata University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Keywords | 2次元特異点 / 幾何種数 |
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| Outline of Final Research Achievements |
The aim of this research is to study fundamental analytic invariants and the structure of normal surface singularities. For Brieskorn complete intersection singularities, we obtained a formula of the normal reduction number of maximal ideals and classified the elliptic singularities. We gave examples of certain distinguished structures of singularities which are homeomorphic to a Brieskorn complete intersection singularity. For cone singularities, we obtained a simple formula of the normal reduction number. We also introduced elliptic ideals and strongly elliptic ideals and obtained their basic properties.
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| Free Research Field |
複素特異点論
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| Academic Significance and Societal Importance of the Research Achievements |
代数多様体や複素解析空間には特異点が存在する．特異点の性質を捉えることで，それらの深い理解につながることがある．本研究は2次元特異点を対象に，基本的な解析的不変量や特異点の構造について，より詳しい結果を得るとともに，新たな研究課題を見出している．これらの成果はこれからの研究の進展に寄与するものと思われる．
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