2005 Fiscal Year Final Research Report Summary
A study on the singular Fano compactifications of 3-dimensional complex affine spaces
| Project/Area Number |
16540074
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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 |
Geometry
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| Research Institution | Kumamoto University |
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Principal Investigator |
FURUSHIMA Mikio Kumamoto University, Department of Science, Professor, 理学部, 教授 (00165482)
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| Co-Investigator(Kenkyū-buntansha) |
ABE Makoto Kumamoto University, Department of Medical Science, Associate Professor, 医学部, 助教授 (90159442)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Affine spaces / Compactifications / Fano |
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| Research Abstract |
We study the classification of the singular Fano 3-fold with the Picard number one which is a compactification of complex affine space C^3. Let r(0<r<5) be the index of such a Fano compactification. In our study, we can determine the structure for the cases of r=2,3 and 4. Moreover we construct a non-trivial example of the singular Fano compactification of C^3, which will be helpful for the determination of the case of the index r=1. We also get two results in the relation with the compactiication of affine spaces.
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