Differential Equations with singularities on free divisors and related Geometry
| Project/Area Number |
17K05269
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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 |
Basic analysis
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| Research Institution | Tokyo University of Agriculture and Technology |
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Principal Investigator |
Sekiguchi Jiro 東京農工大学, 工学(系)研究科(研究院), 名誉教授 (30117717)
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| Project Period (FY) |
2017-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | WDVV方程式 / 代数的ポテンシャル / 実鏡映群 / 複素鏡映群 / 単純特異点 / potential vector field / 拡張WDVV方程式 / ポテンシャル・ベクトル場 / パンルベVI方程式 / パンルベ方程式 / フロベニウス多様体 / 平坦構造 |
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| Outline of Final Research Achievements |
The principal researcher of this research studied mainly two subjects.
The first subject concerned with the construction of potential vector fields of
flat structures. The flat structure is a generalization of Frobenius manifolds established by the principal researcher and collabolators Mitsuo Kato and Toshiyuki Mano. There are two interesting examples of such structure. One is related to Painleve VI equation and the other is related to complex reflection groups. Concerning to these examples, we constructed corresponding potential vector fields. The second subject is the construction problem of algebraic potentials of Frobenius manifolds. The principal researcher constructed some examples of such potentials and in particular showed an interesting relationship between two examples related with reflection groups of types E6 and E7 and complex reflection groups No.33 and No.34. As a consequence an answer to the Arnold Problem on complex reflection groups are given to these two groups.
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| Academic Significance and Societal Importance of the Research Achievements |
フロベニウス多様体の一般化である平坦構造の構成、その中心的対象であるポテンシャルベクトル場の構成とパンルベVI方程式の代数解との対応の明確化、また複素鏡映群の場合のポテンシャルの存在と構成について基本的な成果が得られた。平坦構造の重要性についての意義を与えることができた。代数的フロベニウス多様体のポテンシャルの例の構成はあまりなかったが、本研究ではいくつかの例を構成できた。本研究の意義は、代数的フロベニウス多様体と複素鏡映群との関係を与えたこと、1970年代に定式化された複素鏡映群についてのアーノルドの問題に対する進展を得たことである。
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Report
(7 results)
Research Products
(26 results)
