Deformations of curves on a uniruled variety and their obstructions
| Project/Area Number |
25400048
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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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) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 無限小変形 / ヒルベルトスキーム / 障害類 / ４次超曲面 / K3曲面 / ファノ多様体 / 有理曲線 / 楕円曲線 / ４次曲面 / 変形理論 / 空間曲線 / 3次曲面 |
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| Outline of Final Research Achievements |
We study the deformations of a smooth curve C on a smooth projective threefold V, assuming the presence of an intermediate smooth surface S between C and V. Generalizing a result of Mukai and Nasu, we give a new sufficient condition for a first order infinitesimal deformation of C in V to be primarily obstructed. In particular, when V is Fano and S is K3, we give a sufficient condition for C to be (un)obstructed in V, in terms of (-2)-curves and elliptic curves on S. Applying this result, we prove that the Hilbert scheme of smooth connected curves on a smooth quartic threefold contains infinitely many generically non-reduced irreducible components.
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Report
(4 results)
Research Products
(17 results)
