Complex analytic geometry on the holomorphic branched covering structure
| Project/Area Number |
23540202
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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 | Nara Women's University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
FUJIMURA Masayo 防衛大学校, 総合教育学群, 講師 (00531758)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 複素解析学 / 正則分岐被覆 / モジュライ・パラメーター / モジュライ空間 / コンパクト化 / 国際情報交換 / 正則被覆構造 / 変形空間 / 国際研究者交流 |
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| Outline of Final Research Achievements |
We establish the theory on compactification of the dynamical moduli spaces for rational functions almost completely. This is one of the main purposes of this research project. Actually, the main purpose is geometric construction of compactification for the deformation spaces of holomorphic branched covering structures and explicit formulation of degeneration and bifurcation of them from the viewpoint of complex geometry. This is acheived for the holomorphic branched covering structure induces by rational functions.
Next, by using cross-ratio coordinates as moduli parameters, not only for finitely generated Moebius groups, but also for iterated function system by contracting self-similarities, we give complete description of the deformation spaces, and clarify the relation between compactification of them and the Teichmuller theory. It is the other main purpose of this project.
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Report
(5 results)
Research Products
(11 results)
