| Project/Area Number |
15K04810
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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 | The University of Electro-Communications |
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Principal Investigator |
Ohno Masahiro 電気通信大学, 大学院情報理工学研究科, 准教授 (70277820)
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| Co-Investigator(Kenkyū-buntansha) |
寺川 宏之 都留文科大学, 教養学部, 教授 (80277863)
山口 耕平 電気通信大学, 大学院情報理工学研究科, 教授 (00175655)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | ベクトル束 / ネフ / 大域生成 / ネフなベクトル束 / 導来圏 / 半直交分解 |
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| Outline of Final Research Achievements |
We work over an algebraically closed field of characteristic zero. First we classified nef vector bundles on a smooth projective quadric surface with first Chern class (2,1). They consist of 5 types of vector bundles and they are all globally generated. Second we classified nef vector bundles on a projective space with first Chern class three. Note here that in this case the second Chern class is non-negative and less than or equal to nine. We showed in particular that if the second Chern class is less than or equal to seven, then they are all globally generated, and that if the second Chern class is eight, then they are not globally generated and they exist only on a projective plane.
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| Academic Significance and Societal Importance of the Research Achievements |
ベクトル束の性質に，大域生成と呼ばれる幾何学的な性質と，ネフ(nef, 数値的半正)と呼ばれる数値的な性質がある．一般に，大域生成ならばネフだが，この逆は成り立たない．一方，不変量等の数値的な条件から幾何学的状況をどれだけ回復できるか？という観点から，どのような条件のもとでネフならば大域生成がわかるか？は興味の持たれるところである．本研究の研究成果は特にこの観点からの学術的意義があると考えている．
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