2017 Fiscal Year Final Research Report
Studies on cusp singularities by the theory of formal fans
| Project/Area Number |
15K13423
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 代数幾何学 / 代数多様体 / トーリック多様体 / カスプ特異点 / 扇 / 形式スキーム |
|---|
| Outline of Final Research Achievements |
For the toric type cusp singularities which are described by the theory of toric varieties, we tried to establish the theory of formal fans. We defined fixed formal fans and found a sufficient condition on a support function so that such a formal fan to be a fan in a classical sense. For a 4-dimensional example of cuspsingularity obtained by Tsuchihashi, we described explicitly the intersections of the four exceptional divisors at 48 ordinary quadruple points. We described toric type cusp singularities and their resolutions, which are originally defined as complex analytic isolated singularities, over a field of any characteristic by using the theory of formal schemes. They are realized as complete local rings and projective schemes over them.
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| Free Research Field |
代数幾何学
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