2010 Fiscal Year Final Research Report
Deformations of curves on a higher dimensional algebraic variety and their obstructions
| Project/Area Number |
21740029
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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 |
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Principal Investigator |
NASU Hirokazu Tokyo Denki University, 情報環境学部, 助教 (30535331)
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| Project Period (FY) |
2009 – 2010
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| Keywords | ヒルベルトスキーム / 変形理論 / 空間曲線 / 無限小変形 / 障害 |
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| Research Abstract |
In this project, we investigated infinitesimal deformations of curves on a higher dimensional algebraic variety and their obstructions, and non-reduced components of the Hilbert scheme. As a result, we have proved a conjecture due to Kleppe and Ellia, which is concerned with non-reduced components of the Hilbert scheme of space curves, in the case where a general member of the components are quadratically normal. We also study the deformations of degenerate curves on a higher dimensional scroll, and construct a family of curves, which have a first order deformation not liftable to the second order deformation.
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