| Project/Area Number |
26400083
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
YAMAGUCHI Kohhei 電気通信大学, 大学院情報理工学研究科, 教授 (00175655)
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| Co-Investigator(Kenkyū-buntansha) |
Guest Martin (GUEST Martin) 早稲田大学, 理工学術院, 教授 (10295470)
山田 裕一 電気通信大学, 大学院情報理工学研究科, 教授 (30303019)
島川 和久 岡山大学, 自然科学研究科, 特命教授 (70109081)
大野 真裕 電気通信大学, 大学院情報理工学研究科, 准教授 (70277820)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ホモトピー型 / 正則写像 / 複素多様体 / 実代数的多様体 / トーリック多様体 / 終結式 / 手術 / 実特異点 / 実代数多様体 / 代数幾何学 / チャーン類 / 絡み目 / ホモトピー論 / 実代数幾何学 / ベクトル束 / ホモロジー群 / ホモトピー群 / 圏 |
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| Outline of Final Research Achievements |
For complex manifolds X and Y (resp. real algebraic varieties X and Y), let Hol(X,Y) (resp. Alg(X,Y)) denote the space of holomorphic maps (resp. algebraic maps represented by polynomials) from X to Y. In this situation, we consider the inclusion map from Hol(X,Y) or Alg(X,Y) into the space Map(X,Y) of all continuous maps from X to Y, and we would like to investigate what dimension this inclusion map approximates the infinite dimensional space Map(X,Y). This problem is called the Atiyah-Jones-Segal conjecture. In particular, in this research we generalize the result of G. Segal concerning to the space of rational functions.
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