Research on duality theorems of modules on fans
| Project/Area Number |
12640006
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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 University |
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Principal Investigator |
ISHIDA Masanori Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30124548)
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| Co-Investigator(Kenkyū-buntansha) |
KAJIWARA Takeshi Tohoku University, Graduate School of Science, Research Assistant, 大学院・理学研究科, 助手 (00250663)
ITO Hiroyuki Hiroshima University, Graduate School of engineering, Associate Professor, 大学院・工学研究科, 助教授 (60232469)
HARA Nobuo Tohoku University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (90298167)
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| Project Period (FY) |
2000 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | algebraic variety / toric variety / abelian variety / elliptic curve / blowup / Rees alebra / fan / 可換環 / 楕円曲面 / 強レフシェッツ定理 / K3曲面 / 双対化定理 / 交叉コホモロジー群 / 端末特異点 |
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| Research Abstract |
Ishida studied on not necessarily rational fan as a generalization of the theory of toric varieties. He constructed the theory of Zariski-Riemann spaces of fans.
Hara defined the tight closure of ideals associated with a fixed ideals as a generalization of the theory of tight closures of ideals.
Ito studied on the Mordell-Weil lattices of elliptic curves from the view point of singularity theory and deformation theory.
Kajiwara studied on the Deligne conjecture on the l-adic etale cohomology of nonsingular algebraic varieties defined over a valuation ring.
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Report
(5 results)
Research Products
(23 results)
