Study of vector bundles on algebraic varieties
| Project/Area Number |
19540034
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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 | Hiroshima University |
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Principal Investigator |
SUMIHIRO Hideyasu Hiroshima University, 大学院・理学研究科, 名誉教授 (60068129)
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| Co-Investigator(Kenkyū-buntansha) |
ISHII Akira 広島大学, 大学院・理学研究科, 准教授 (10252420)
KIMURA Shunichi 広島大学, 大学院・理学研究科, 准教授 (10284150)
KITADAI Yukinori 広島大学, 大学院・工学研究科, 特任助教 (30511563)
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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 | 代数幾何学 / 代数学 / ベクトル束 / Frobenius写像 / ベクトル束の分解問題 / Hartshorne予想 / 小平消滅定理 / ペクトル束 |
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| Research Abstract |
Lange-Pauly proved that the direct images of line bundles on non-singular projective curve with genus greater than or equal 2 are semi-stable. We extended this result to semi-stable vector bundles on non-singular curves and non-singular projective surfaces. As a corollary, we get a new result on geography of non-singular minimal surfaces of general type in positive characteristics. Further, We obtained a new theorem for rank two vector bundles on 4-dimensional projective space to split into line bundles.
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Report
(4 results)
Research Products
(23 results)
