The structure of affine algebraic varieties and the Linearization Problem
| Project/Area Number |
18540045
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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 | University of Hyogo |
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Principal Investigator |
MASUDA Kayo University of Hyogo, 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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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,060,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥660,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | 加法群 / locally nilpotent derivation / アファイン空間 / トーラス群 / 埋め込み / embedding / equivariant vector field / generalized Jacobian Problem / additive group action / G_a-action / Makar-Limanov invariant / affine surface / polynomial ring / affine pseudo-plane / torus action / Jacobian conjecture / G-endomorphism |
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| Research Abstract |
We studied the structure of affine algebraic varieties from the viewpoint of the actions of algebraic groups, especially the additive group. We gave a description of the structure of the affine surfaces of some type including the affine pseudo-plane. We show that there exists a close relationship among the big three open problems -- the Linearization Problem, Cancellation Problem, and the Embedding Problem-- through the action of the additive group. Further, we gave a characterization of the affine space of higher dimension in some cases by the algebraic actions.
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Report
(6 results)
Research Products
(61 results)
