Relations between free resolutions and the arithmetical rank for a monomial ideal
| Project/Area Number |
24740008
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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 | Shizuoka University |
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Principal Investigator |
KIMURA Kyouko 静岡大学, 理学(系)研究科(研究院), 講師 (60572633)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 算術階数 / 射影次元 / 極小自由分解 / ベッチ数 / エッジイデアル / regularity / マッチング数 / Gorensteinイデアル |
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| Outline of Final Research Achievements |
We study a squarefree monomial ideal of a polynomial ring over a field. The main theme of the project is to clarify relations between the arithmetical rank of the ideal, especially a construction of elements which generate the ideal up to radical, and a free resolution of its quotient ring. We proved that the arithmetical rank is equal to the projective dimension for a Gorenstein squarefree monomial ideal of height 3 (joint work with Naoki Terai) and a squarefree monomial ideal whose associated hypergraph is a string or a cycle (joint work with Paolo Mantero).
Another theme of the project is the study of a minimal free resolution of an edge ideal. We obtain some results, for example, a new sufficient condition for the non-vanishing of the Betti numbers of an edge ideal.
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Report
(4 results)
Research Products
(20 results)
