2014 Fiscal Year Final Research Report
Study on vector bundles, D-modules and harmonic bundles
| Project/Area Number |
22540078
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Keywords | 調和バンドル / ツイスターD加群 / ホロノミックD加群 / 戸田格子 / インスタントン / ベッチ構造 |
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| Outline of Final Research Achievements |
I published a monograph on the study of wild harmonic bundles and pure twistor D-modules. I introduced the concepts of mixed twistor structure and Betti structure on holonomic D-modules, and established their functoriality with respect to various standard operations. I applied the ideas and the results in the theory of wild harmonic bundles to the study of doubly periodic instantons and 2-dimensional Toda equations. I studied the asymptotic behaviour of doubly periodic instantons by regarding them as infinite dimensional harmonic bundles. On the basis of the result, I established that the Nahm transform give an equivalence between wild harmonic bundles on elliptic curve and doubly periodic instantons. As for the Toda equations, I observed an equivalence of solutions of the Toda equations and some type of harmonic bundles, which was useful for the classification of the solutions. I also computed the Stokes structure of the associated meromorphic flat bundles.
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| Free Research Field |
微分幾何
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