| Project/Area Number |
15K17513
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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 | The University of Tokushima |
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Principal Investigator |
Nabeshima Katsusuke 徳島大学, 大学院社会産業理工学研究部(理工学域), 准教授 (00572629)
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| Research Collaborator |
TAJIMA Shinichi 筑波大学, 数理物質系(数学域), 教授
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 代数的局所コホモロジー / 孤立特異点 / アルゴリズム / 包括的グレブナー基底系 / Limiting tangnet space / 変形チュリナ数 / local Euler obstruction / 特異点 / 対数的ベクトル場の計算 / Bernstein-佐藤多項式 / グロタンディーク留数 / 特異点変形アルゴリズム / 代数的局所コホモロジー類 / b-関数 / ミルナー数の列 / limiting tangent space / D加群 / 局所コホモロジー / 対数的ベクトル場 / チュリナ数 / ミルナー数 / グレブナー基底 / パラメータ付きシステム |
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| Outline of Final Research Achievements |
We have given algorithms and implementations for computing invariants of hypersurface isolated singularities (i.e., Limiting tangent space, μ*-sequence, integral number, local Euler obstruction, Tjurina stratifications of μ-constant deformations). Furthermore, we have introduced algorithms for solving ideal membership problems in local rings and computing comprehensive Groebner systems in PBW algebras. These algorithms are useful to study hypersurface singularities.
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