| Project/Area Number |
19540037
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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 Kyushu University, 大学院・数理学研究院, 教授 (10112278)
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| Co-Investigator(Kenkyū-buntansha) |
古島 幹雄 熊本大学, 理学部, 教授 (00165482)
高山 茂晴 東京大学, 大学院・数理科学研究科, 准教授 (20284333)
横山 和弘 立教大学, 理学部, 教授 (30333454)
朝倉 政典 九州大学, 大学院・数理学研究院, 助教 (60322286)
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| Co-Investigator(Renkei-kenkyūsha) |
FURUSHIMA Mikio 熊本大学, 理学部, 教授 (00165482)
YOKOYAMA Kazuhiro 立教大学, 理学部, 教授 (30333454)
TAKAYAMA Shigeharu 東京大学, 大学院・数理科学研究科, 准教授 (20284333)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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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 |
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| Research Abstract |
For the study of higher dimensional algebraic varieity X we take a hyperplane section A of X for the use of Lefschetz Theorem and try to find the structure of X by the one of A.This time we studied whether the bundle structure of A is preserved to X and next the structure of blowing-up is also so. Moreover generalizing the method,we investigate the preservation of the extremal ray.As applications we get the following : Theorem. Let us consider a sequence {X_n} of smooth projective varieties so that X_n s an ample divisor in X_{n+1} for each n. Here n runs over each positive integer. Assume X_1 has an elementary contraction f : X_1 -> Y with dim X_1 - dim Y > 1 and dim X_1 > 2.Then for each n there is an inductively extended morphism f_n : X_n -> Y with f_{n-1}=i_{n-1}f_n where i_{n-1} : X_{n-1} -> X_{n} is a natural embedding. For a very general point y of Y a smooth fiber of f_n is a weighted complete intersection for large enough n.The above theorem says that a variety enjoying a sequence {X_n} of smooth projective varieties has the structure of property "symmetry".
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