| Project/Area Number |
16540049
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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 | Kitami Institute of Technology |
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Principal Investigator |
YAMADA Hiroshi Kitami Institute of Technology, 工学部, Technology Professor (50210472)
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Norio Kitami Institute of Technology, 工学部, associated Professor (80211986)
WATANABE Fumihiko Kitami Institute of Technology, 工学部, associate Professor (20274433)
IOHARA Kenji Kobe University, 理学部, assistant (00322199)
KAWAI Shingo Tokyo Institute of Technology, 理学研究科, assistant (60302931)
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| Project Period (FY) |
2004 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | elliptic curve / unstable holomorphic G-bundles / stable holomorphic G-bundles / simply elliptic singularity / anti-holomorphic connections / Lie group / affine Lie group / double loop algebra / double loop群 / kouble loop algebra / 不安定G-束 / 安定G-束 / モジュライ / パンルベ方程式 / 単純特異点 / 不安定ベクトル束 / double loon algebra / 単純楕円型特異点 / 初期値空間 |
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| Research Abstract |
In this research, we showed the existence of non-trivial holomorphic functions on C^*-bundle on the double loop algebra E (g) which is invariant under a twisted gauge transformation of the double loop group E (G). Using these E (G)-invariant holomorphic functions, we gave a characterization of holomorphic unstable principal G-bundles over an elliptic curve. Furthermore, we classify the isomorphism classes of holomorphic semi-stable G-bundles over an elliptic curve.
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