Application of New Methods of Combinatorial Topology to Commutative Algebra
| Project/Area Number |
25400057
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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 | Kansai University |
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Principal Investigator |
Yanagawa Kohji 関西大学, システム理工学部, 教授 (40283006)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 組合せ論的可換代数 / 単項式イデアル / Lyubeznik 数 / 極小自由分解 / CW胞体 / 有向マトロイド / アファイン有向マトロイド / 正則CW複体 / 局所コホモロジー / cd指数 |
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| Outline of Final Research Achievements |
With Spanish and American coauthors, I studied the Lyubeznik numbers of the quotient rings of polynomial rings by monomial ideals. For example, we showed that the procedure of "polarization" essentially preserves this invariant. With Prof. S. Murai, I studied the "cd-index" of flag complexes using the notion of squarefree modules. I also studied cellular free resolutions of monomial ideals with Prof. R. Okazaki. We applied this method to the study of affine oriented matroids.
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Report
(4 results)
Research Products
(13 results)
