On families of rational curves and Fano varieties.
| Project/Area Number |
22540050
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
SATO Eiichi 九州大学, 大学院・数理学研究院, 学術研究者 (10112278)
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| Co-Investigator(Renkei-kenkyūsha) |
WENG Lin 九州大学, 大学院・数理学研究院, 教授 (60304002)
TAKAYAMA Shigeharu 東京大学, 大学院・数理科学研究科, 教授 (20284333)
TAKAGI Shunsuke 東京大学, 大学院・数理科学研究科, 准教授 (40380670)
FUKUMA Yoshiaki 高知大学, 理学部, 准教授 (20301319)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 有理曲線 / 単有理性 / ファノ多様体 / コニック束 / レフシェッツの超平面切断研究分野 / ﾚﾌｼｪｯﾂの超平面切断 / レフシェッツの超平面切断 |
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| Research Abstract |
The reporter studied under what conditions a surjective morphism f: X -> Y is locally trivial or isomorphic. It is important and effective toclassify the world of Fano varieties. In the formar case assuming that the anti-relative canonical line bundle -K_f (:= -K_X -f*K_Y) of the morphism f is nef,we can show f is locally trivial. Especially in case of the smoothness of f assuming that a general fiber is Del pezzo surface or a smooth hypersurface,we get the same results. In the latter case if X is an n(> 2)-dimensional cubic hypersurface, f is an isomorphism unless Y is a projective space or a hyperquadric.
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Report
(4 results)
Research Products
(35 results)
