Analysis of freeness of multiarrangements and generation of related geometry
| Project/Area Number |
21740014
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
ABE Takuro 京都大学, 大学院・工学研究科, 講師 (50435971)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 超平面配置 / 代数幾何 / 自由配置 / 対数的ベクトル場 / 多重配置 / コクセター群 / ベッチ数 / 有向グラフ / ルート系 / 原始微分 / ベクトル束 / フロベニウス多様体 |
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| Research Abstract |
In this research program, we aimed at the deep understanding of free multiarrangements the study of which is developing in these days. Also, to find related geometry to them is one of purposes. As a result, in particular for Coxeter arrangement cases, we could understand the freeness deeply by using the invariant theory of Coxeter groups. Also, we relate the freeness of arrangements to that of its Ziegler restriction and the second betti number, or the minimality of chambers under the assumption of tameness. Moreover, by relating the freeness of line arrangements to the minimality of chambers, we find a geometric aspect of freeness.
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Report
(4 results)
Research Products
(38 results)
