Analysis of freeness of hyperplane arrangements and related geometry
| Project/Area Number |
24740012
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyushu University (2015)
Kyoto University (2012-2014) |
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Principal Investigator |
Abe Takuro 九州大学, マス・フォア・インダストリ研究所, 准教授 (50435971)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 超平面配置 / 自由配置 / 代数学 / 代数幾何学 / ベクトル束 / ルート系とワイル群 / イデアル / 直線配置 / 剰余的自由配置 / コホモロジー環 / ルート系 / 指数 / イデアル配置 / ルートの高さ分布の双対分割 / 分裂型 / 自由配置の剰余定理 / ワイル群 / 対数的ベクトル場 / 指標 / 高さ分布の双対分割 / Shi配置とCatalan配置 / 原始微分 / 加除定理 |
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| Outline of Final Research Achievements |
This research program aims at studying the freeness of hyperplane arrangemens more deeply, and investigate its geometry. These aims are achieved and the results are better than we expected. First, for any ideal subarrangements of Weyl arrangements coming from an ideal which is certain subsets of positive roots, we determine its Betti numbers by using freeness which coincides with the dual partition of height distributions of roots in the ideal. Next, we improved Terao's addition-deletion theorem invented in 1980 into the division theorem for free arrangements. By applying it, we enlarged the class in which the freeness depends only on combinatorics, and named divisionally free arrangements. These two results are of the great advances in this research area, so we think this research program is achieved successfully.
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Report
(5 results)
Research Products
(40 results)
