2014 Fiscal Year Final Research Report
Application of discrete Morse theory with commutative algebra
| Project/Area Number |
24740013
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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 | Fukuoka University of Education (2013-2014)
Osaka University (2012) |
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Principal Investigator |
OKAZAKI Ryota 福岡教育大学, 教育学部, 講師 (20624109)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | Cellular 自由分解 / 離散モース理論 / 正則 CW 複体 / アフィン有向マトロイド / bounded complex / 多重次数付き加群 / 根基 |
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| Outline of Final Research Achievements |
By a study with K. Yanagawa, we've proved that for a Cohen-Macaulay Borel-fixed ideal, its two different graded minimal free resolutions ― Eliahou-Kervaire resolution and the one given by our previous work ― are supported by cellular decompositions (distinct in general) of a closed ball. These resolutions are constructed by applying discrete Morse theory (DMT); the result above can be considered as a reconstruction of geometrical information lost (obscured) by application of DMT.
Besides, the following have been achieved: Construction of a free resolution of a multigraded module: Defining its radical of them by using a functor to generalize known results for monomial ideals (with V. Ene): Characterization of Cohen-Macaulay-ness of the bounded complex and the matroid ideal of an affine oriented matroid (with K. Yanagawa).
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| Free Research Field |
組合せ論的可換代数
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