Algebraic geometry of hypersurfaces and lines in projective spaces and Hodge structure
| Project/Area Number |
20740014
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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 | Tokyo Denki University (2011)
Osaka University (2008-2010) |
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Principal Investigator |
IKEDA Atushi (IKEDA Atsushi) 東京電機大学, 工学部, 准教授 (40397617)
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 代数幾何 / ホッジ構造 / 3次曲面 / 周期写像 / 3次超曲面 |
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| Research Abstract |
We described geometric property of a hypersurface in a projective space by using the Hodge structure of the variety of lines which intersect the hypersurface with some multiplicity. We explained the relation between geometric property of lines in cubic surface and the Neron-Severi lattice of the variety of lines, and we computed the structure of the Neron-Severi lattice. And we showed the injectivity of the period map which is defined by the Hodge structure of variety of lines form the family of cubic surfaces over the moduli space.
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Report
(6 results)
Research Products
(22 results)
