2022 Fiscal Year Final Research Report
| Project/Area Number |
16H03932
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Keywords | ツイスター空間 / 二重被覆写像 / 双有理変換 / 有理多様体 |
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| Outline of Final Research Achievements |
The twistor spaces associated with 4-dimensional compact self-dual manifolds are 3-dimensional compact complex manifolds. Most of them do not admit a Kahler metric, and moreover, they are known to be non-algebraic (in the sense that they are not bimeromorphic to projective algebraic varieties). In this study, we investigate the structure of compact twistor spaces that do not have a Kahler metric but are algebraic (in the sense that they are bimeromorphic to projective algebraic varieties). For any given twistor space, there is a linear system called the fundamental system, and it was known that the structure of the twistor space is considerably limited by the structure of a divisor belonging to the fundamental system. In this study, we obtained a structure theorem for algebraic compact twistor spaces such that the fundamental system is of dimension one or more.
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| Free Research Field |
幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
自己双対計量とツイスター空間の研究はペンローズにより、物理現象を複素数を用いた幾何学、すなわち複素幾何により理解する目的で始められたが、そこで見出された方法や対象は純粋数学においても多くの応用や成果をもたらした。本研究はツイスター理論を純粋数学における対象として考察するものである。このような研究は世界的に見てあまりなされておらず、独自性があるものだと思われる。また本研究で最終的に得られた構造定理は（当初の予想に反して）かなりシンプルなものである。
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