The structure of affine algebraic varieties and the additive group actions
| Project/Area Number |
22540059
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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 | Kwansei Gakuin University |
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Principal Investigator |
MASUDA Kayo 関西学院大学, 理工学部, 教授 (40280416)
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| Co-Investigator(Kenkyū-buntansha) |
MIYANISHI Masayoshi 関西学院大学, 数理科学研究センター, 客員研究員 (80025311)
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| Co-Investigator(Renkei-kenkyūsha) |
KURODA Shigeru 首都大学東京, 理工学研究科, 准教授 (70453032)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | アファインファイブレーション / 加法群 / 代数群 / 加法群の作用 / 局所べき零微分 / アフィン代数多様体 / 代数群の作用 / ファイブレーション / 代数幾何学 / トーラス群の作用 / A^1-fibration / affine threefold / derivation / A^1_*-fibration / quotient morphism / quotient / locally nilpotent derivation |
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| Outline of Final Research Achievements |
In affine algebraic geometry, affine space is the most fundamental and important object. However, we have not obtained the algebro-geometric characterization of affine space of higher dimension. In this project, trying to provide characterizations of affine spaces among algebraic varieties, we investigated the additive group actions on algebraic varieties of three or higher dimension, and succeeded in determining the structure of three-dimensional algebraic varieties in some cases.
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Report
(6 results)
Research Products
(45 results)
