2010 Fiscal Year Final Research Report
Resolution of Singularities of an algebraic varieties defined over an algebraically closed field
| Project/Area Number |
20740012
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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 | Kyoto University |
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Principal Investigator |
KAWANOUE Hiraku Kyoto University, 数理解析研究所, 助教 (50467445)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 代数幾何学 / 特異点解消 / 正標数 / IFP |
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| Research Abstract |
To solve the problem of resolution of singularities, a longstanding open problem in algebraic geometry, the author developed his own program, called IFP. He defined an invariant for resolution in the framework of IFP, and show that it behaves quite well in the situation before blowups. Moreover, by examining the properties for the expected behavior of invariants through blowups, he found the possibility of the better invariant using strict transforms, and obtained some partial results concerning it.
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