Application of commutative algebra to topological study on affine oriented matroids
| Project/Area Number |
16K05114
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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) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 組合せ論的可換代数 / アファイン有向マトロイド / Cohen-Macaulay 性 / Cohen-Macaulay性 / Specht ideal / コーエン・マコーレー環 / 極小自由分解 / Ｃｏｈｅｎ－Ｍａｃａｕｌａｙ性 |
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| Outline of Final Research Achievements |
Just before this project started, the author and his coworker (almost ) showed that if the ideal associated with an affine oriented matroid M is Cohen-Macaulay (CM,for short), then the bounded complex of M is a contractible homology manifold (with boundary). In this situation, we conjectured that the bounded complex is homeomorphic to a closed ball. This conjecture is the main aim of this project. Finally, we proved the conjecture when the dimension is at most 3. We also showed that the bounded complex is a topological manifold in the dimension 4 case.
In the latter period of this project, the Specht ideals have been a main object of the study.We completely determined the CM Specht ideals in the characteristic 0 case.
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| Academic Significance and Societal Importance of the Research Achievements |
数学の基礎研究であり、基本的には純粋な学術的価値を追求するものである。たとえば、主たる目的とした予想は、かつて「Zaslavsky予想」と呼ばれた比較的有名な問題(現在は、Dong によって解決されている)の一般化を図るものであった。
ただ、有向マトロイドは応用数学の範疇に属する研究対象であり、今回の結果は純粋数学からのアプローチではあるが、将来的・間接的には何らかの応用が見つかる可能性が有る。
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Report
(5 results)
Research Products
(10 results)
