A study on compactifications of complex affine planes and spaces
| Project/Area Number |
22540051
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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 |
Algebra
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| Research Institution | Kumamoto University |
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Principal Investigator |
FURUSHIMA Mikio 熊本大学, 大学院・自然科学研究科, 教授 (00165482)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 代数幾何学 / コンパクト化 / 端末特異点 / ファノ空間 / アフィン平面 / アフィン空間 / ファノ多様体 |
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| Research Abstract |
(1) Research 1: The boundary of compactification of C^2 into Hirzebruch surfacesconsists of two irreducible components, one of which can have a singularity byL.Brenton. Then I can construct more general examples including the Brenton’ s one. Ialso prove that one of the irreducible components of boundary divisor is a smoothrationa curve. Further , I suggested the possibility of a birational geometric proof of thetheorem by Abyankar-Moh- Suzuki. (2) Research 2: I studied the detail structure of singular Fano threefolds withGorenstein terminal singularities as a compactification of C^2.,especially , applying thetheory of smoothing of Fano threefolds with Gorenstein terminal singularities, I candetermine the detail structure of the known examples of singular Fanocompactifications of C^3..
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Report
(4 results)
Research Products
(13 results)
