| Project/Area Number |
14540039
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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 |
ASHIKAGA Tadashi Tohoku-Gakuin University, Faculty of Engineering, Professor, 工学部, 教授 (90125203)
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| Co-Investigator(Kenkyū-buntansha) |
KONNO Kazuhiro Tohoku-Gakuin University, Mathematical Institute of Graduate school of Osaka University, Professor, 大学院・理学研究科, 教授 (10186869)
TSUCHIHASHI Hiroyasu Tohoku-Gakuin University, Faculty of general Education, Associate Professor, 教養学部, 助教授 (00146119)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2002: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | Degeneration / Signature / Monodromy / Localization / Families of algebraic carves / Stable reduction / Pedeking Sum / Fixed point theorem / 安定環元 / 局所符号数 / 半安定環元 / 曲線束 / デデキント和 / 同変指数定理 / 代数曲面 / 局所集中性 |
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| Research Abstract |
The aim to obtain an explicit formula of local signature for the contribution of semi-stable reduction coas completed by applying Atiyah-Singer's G-signature theovem, The main termof the formula consists of Pedeking sams of Nielsen-Matsumoto-Moutesions' monodromy data, and I wrote it in Kokyuroku RIMS1345(2003), PP.203-237.
The aim to compare Furuta's local signature and Yoshikawa's local signature was almost settled, and I wrote it in the previous RIMS report. But Yoshikawa critacize a cerlain part of the argument, and my study in still on the way at this point.
On the other hand, I also obtained a formula for the contribution of semi-stavle reduction to Yoshikawa's local signature by using Atiyah-Botl-Segal-Singer's fixed point formula, and I gave a lecture forit at the symposium "Algobraic Geomety and Topoloy of Hodge Theory, Degnerations and Complex Sarface", I am preparing the full paper of these results.
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