Signature divisor on the moduli of curves, signature defect and its applications
| Project/Area Number |
21540047
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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 |
Algebra
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| Research Institution | Tohoku Gakuin University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
YOSHIKAWA Ken-ichi 京部大学, 大学院・理学研究科, 教授 (20242810)
KONNO Kazuhiro 大阪大学, 大学院・理学研究科, 教授 (10186869)
ISHIDA Hirotaka 宇部工業高等専門学校, 一般科, 准教授 (30435458)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 符号数 / モジュライ空間 / モノドロミー / 退化 / 局所化 / 複素曲面 / ファイバー空間 / 安定還元 / 特異点 / デデキンド和 / 連分数 / モジュライ写像 / ファイバー芽 / エータ不変量 / モジュライ |
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| Research Abstract |
We have a new formulation of the local signature of a fiber germ of degeneration of curves as a sum of "moduli term" and "monodromy term" in the following sense.
The former is defined as the pull back by the moduli map of the signature divisor on the moduli space of stable curves(joint work with Ren-ichi Yoshikawa).
The latter is called local signature defect, which is obtained via the orbifold signature theorem by interpreting the topological monodromy data as a group action to the stable reduction.
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Report
(4 results)
Research Products
(56 results)
