Geometry of Degenerations of Riemann Surfaces
| Project/Area Number |
20540073
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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) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | リーマン面 / 分裂変形 / 複素曲面 / 特異点 / モノドロミー / リーマン面の退化 / デーン・ツイスト / 複素幾何 / モジュライ空間 / 退化族 / 複素構造 / デーン・シイスト / テータ関数 |
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| Research Abstract |
We studied degenerations of Riemann surfaces from the viewpoint of low-dimensional topology, algebraic geometry and singular theory. We described holomorphic maps on resolution spaces and described circle actions around the critical sets. We applied these descriptions to those of topological monodromies. Moreover, we generalized a part of these results to the higher-dimensional case. We proved that the quotient of A-singularity under a cyclic group action is uniformized by a small group.
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Report
(6 results)
Research Products
(15 results)
