2009 Fiscal Year Final Research Report
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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| Keywords | 加法群 / locally nilpotent derivation / アファイン空間 / トーラス群 / 埋め込み |
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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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