| Project/Area Number |
19540003
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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 | Tohoku University |
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Principal Investigator |
OGATA Shoetsu Tohoku University, 大学院・理学研究科, 准教授 (90177113)
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| Co-Investigator(Kenkyū-buntansha) |
石田 正典 東北大学, 大学院・理学研究科, 教授 (30124548)
原 伸生 東北大学, 大学院・理学研究科, 准教授 (90298167)
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| Co-Investigator(Renkei-kenkyūsha) |
ISHIDA Masanori 東北大学, 大学院・理学研究科, 教授 (30124548)
HARA Nobuo 東北大学, 大学院・理学研究科, 准教授 (90298167)
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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: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 代数幾何 / トーリック多様体 / 代数幾何学 / ファノ多様体 / 凸体 |
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| Research Abstract |
We classify ample line bundles on nonsingular toric 3-folds whose adjoint bundles are not effective and prove that those ample line bundles are normally generated. We characterize the space of the global sections of the adjoint bundle when it is effective. From this we prove the normal generation of ample line bundle whose adjoint bundle is effective but not big.
We also prove that the multiplication map of global sections of an ample line bundle and a nef line bundle on a singular toric surface is surjective. We may use this surjectivity to investigate normal generation of ample line bundles on a certain singular toric 3-fold.
Moreover, we succeeded to prove that any ample line bundles on toric weak Fano 3-folds are normally generated.
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