2011 Fiscal Year Final Research Report
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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| Keywords | リーマン面 / 分裂変形 / 複素曲面 / 特異点 / モノドロミー |
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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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