2014 Fiscal Year Final Research Report
Applications of minimal model theory to higher dimensional affine algebraic geometry
| Project/Area Number |
24740003
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Saitama University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 極小モデル理論 / アフィン代数多様体 / ユニポテント代数群作用 / affine ruledness |
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| Outline of Final Research Achievements |
Roughly speaking, algebraic geometry deals with two classes of varieties, so-called, projective varieties and affine algebraic varieties. These two classes behave quite differently. The former one, namely, projective varieties can be analyzed by use of several very useful theories, in particular, minimal model theory,which plays remarkably important role for the study of projective varieties from the viewpoint of the behavior of distinguished rational curves. Whereas, as for the latter one, i.e., for affine algebraic varieties, we do not have so far a useful method to investigate them. One of the main reasons to explain this difficulty lies in an impossibility to take a limit over such varieties. To overcome it, we are trying to embed a given affine variety into a projective one in order to apply above mentioned minimal model theory. Of course, several obstacles occur along this attempt, nevertheless we succeed to obtain some useful results.
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| Free Research Field |
代数幾何学
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