2018 Fiscal Year Final Research Report
integrable system and moduli theory of derived category
| Project/Area Number |
26400043
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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 | Kyoto University |
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Principal Investigator |
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| Research Collaborator |
Saito Masa-Hiko
Abe Takeshi
Mochizuki Takuro
Yoshioka Kota
Komyo Arata
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Keywords | モジュライ / 不確定接続 / 一般モノドロミー保存変形 |
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| Outline of Final Research Achievements |
I constructed the moduli space of irreuglar singular connections on algebraic curves. It was difficult to formulate the moduli of ramifeid irregular singular connections, but I succeeded in its formulation and proved that the moduli space of ramified irregular singular connections is smooth with a symplectic structure.
On the other hand, the construction of the unramified irregular singular connections is rather easy and we can construct the generalized isomonodromic deformation based on the Jimbo-Miwa-Ueno theory on the unramified moduli spaces.
I also constructed a deformation of the unramified moduli space to the regular singular moduli spaces and gave a local analytic lift of the generalized isomonodromic deformation.
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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 |
不確定特異点の一般モノドロミー保存変形は，神保・三輪・上野の理論によって確立された可積分系で，ソリトン解を導くなど，幅広い分野へのインパクトを与える理論である．一般モノドロミー保存変形の大域的性質を概念的に捉えるためには、代数曲線上の不確定接続のモジュライ空間で定式化すると明快になる．特に分岐不確定の場合は，モジュライ空間の定式化自体が特に一般種数の場合に非自明であったが，本研究において，局所指数がある種のgenericな条件を満たす場合にその定式化と構成に成功した．
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