2002 Fiscal Year Final Research Report Summary
Topological Study on the Degeneration Phenomena of Riemann Surfaces
| Project/Area Number |
12440013
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | The University of Tokyo |
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Principal Investigator |
MATSUMOTO Yukio The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (20011637)
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| Co-Investigator(Kenkyū-buntansha) |
IMAYOSHI Yoichi Osaka City University, Graduate School of Science, Professor, 理学部, 教授 (30091656)
ASHIKAGA Tadashi Tohoku-Gakuin University, Faculty of Engineering, Professor, 工学部, 教授 (90125203)
FUKUHARA Shinji Tsuda College, Department of Mathematics, Professor, 学芸学部, 教授 (20011687)
AHARA Kazushi Meiji University, School of Science and Technology, Lecturer, 理工学部, 講師 (80247147)
KAWAZUMI Nariya The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (30214646)
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| Project Period (FY) |
2000 – 2002
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| Keywords | Riemann surfaces / degeneration / singular fiber / splitting / monodromy |
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| Research Abstract |
During the term of the project, we have made quite a good progress on the problem of splitting a given complicated singular fiber into a number of simpler singular fibers. Among others, we would like to point out Arakawa and Ashikaga's proof of the splittability of hyperelliptic singular fibers and Takamura's research on the construction of splitting families for not necessarily hyperelliptic singular fibers, Takamura being a cooperative researcher. An experimental method is also very important to the study of splitting of singular fibers. In fact Ahara developed a software "Splitica" by which we can observe the splitting motion of "star-shaped" singular fibers on a computer display. As for the global study of monodromy, Imayoshi, Ito, and Yamamoto made a research from function theoretic viewpoint. Also the quandle of cords which might be important to the study of Lefschetz fibrations, Kamada and Matsumoto studied their algebraic representation. There are obtained many other related results.
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