| Project/Area Number |
16K05116
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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 | Hokkaido University |
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Principal Investigator |
SUWA Tatsuo 北海道大学, 理学研究院, 名誉教授 (40109418)
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| Project Period (FY) |
2016-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 幾何学 / 複素解析幾何学 / 特性類の局所化 / 相対コホモロジー / 局所双対性 / 留数 / 佐藤超関数 / 特異多様体 / ホッジ構造 / 特異葉層構造 / 超関数 |
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| Outline of Final Research Achievements |
The purposes of this research project were to investigate the localization of characteristic classes using relative de Rham, Dolbeault and Bott-Chern cohomologies, to find explicitly the residues obtained via the local duality and to apply these to various problems.
The following are the research achievements: 1. Generalization of the Lefschetz coincidence formula (with J.-P. Brasselet), 2. Theory of relative Bott-Chern cohomollogies and applications (with M. Correa), 3. Behavior of the Hodge structure of a complex manifold under blowing-up (with D. Angella, N. Tardini and A. Tomassini), 4. Simple explicit representation of Sato hyperfunctions and their operations (with N. Honda and T. Izawa).
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| Academic Significance and Societal Importance of the Research Achievements |
数学の研究により得られた知見により文化の発展に貢献する. 本研究代表者が推し進める局所化理論が発展し, さまざまな方面での応用が見出されている. 研究成果の概要欄で述べた成果の内, 特に当初予期されなかったこととして, 佐藤超関数およびそれに関連した演算, 局所双対性等が相対 Dolbeault コホモロジー論を用いると簡明かつ明示的に表せることが分かり, 超関数論の新たな展開を見た. これは複素解析幾何学, 解析学に新たな境地を拓くことが期待される．
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