2011 Fiscal Year Final Research Report
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 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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| Keywords | 代数幾何 / ホッジ構造 / 3次曲面 |
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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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