Splittings of degenerafions of Riemann surfaces
| Project/Area Number |
16540062
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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 |
TAKAMURA Shigeru Kyoto University, Graduate School of Science, Associate Professor (20362436)
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| Project Period (FY) |
2004 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,870,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Riemann surface / splitting / simgularity / monodromy / complex stracture / complex surface / moduli / theta function / モジュライ空間 / 複素構造の変形 / データ関数 |
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| Research Abstract |
Consider a family fo Riemann surfaces with a slaguar fiber (a degeneration), Its topological type is determined by its topological monodromy (Matsumoto-Montesinos Theorem). If the topological monodromy is periodic, then the sluguar fiber is star-shaped ite core with branches, For a particular cure where the core is a Riemann sphere and the number of branches is exactly three, my joint work with Kazushi Ahara (Meiji Univ). Showed that such a degeneration necessarily hao a splitting deformation. The proof is based on my splittability criterion is terms of the existence of a shbdivisor (called a crust) of the singular fiber, The latter work is published an Springer Lecture Notes in Math 1886. We however remark that if the number of braches if at least four, then these is some cate where my criterion does not work, but it' may possibly have a splitting family. this is also a challenging problem to consider.
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Report
(5 results)
Research Products
(8 results)
