Deformations of curves on a higher dimensionalalgebraic variety and their obstructions
| Project/Area Number |
23740032
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Tokai University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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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 / 障害類 / デルペッツォ多様体 |
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| Research Abstract |
We study the first order infinitesimal deformations of degenerate curves on a uniruled algebraic variety of dimension at least 3 and their obstructions. As a result, we give two different geometric interpretations of infinitesimal deformations with poles (rational sections of the normal bundle of hypersurfaces). By using the liaison theory, we give a classification of the irreducible components of the Hilbert scheme for a certain class of space curves. We also study the deformations of space curves lying on a smooth quartic surface of Picard number 2, and construct a new example of families of curves with obstructed first order infinitesimal deformations.
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Report
(3 results)
Research Products
(14 results)
