2010 Fiscal Year Final Research Report
Analysis of structures on affine algebraic varieties from the viewpoint of log minimal model theory
| Project/Area Number |
20740004
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Saitama University |
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Principal Investigator |
KISHIMOTO Takashi Saitama University, 理工学研究科, 准教授 (20372576)
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| Project Period (FY) |
2008 – 2010
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| Keywords | アフィン代数幾何学 / 双有理幾何学 / 加法群スキーム作用 |
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| Research Abstract |
In the present project of research, I devoted mainly myself to the analysis of structures on affine algebraic varieties from the various points of view. More precisely, in the first viewpoint, I succeeded into the translation of the existence of actions of a 1-dimensional additive group on affine cones over polarized projective varieties into the existence of certain kinds of open subset contained in the polarized varieties. In the second, I could reduce the homogeneous action of a 1-dimensional additive group on the affine 3-space to linear pencil of rational curves with special properties on weighted projective planes to be able to produce plenty of complicated automorphisms.
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