Arithmetical rank of Stanley-Reisner ideals and projective dimension of their powers
| Project/Area Number |
26400049
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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 | Saga University |
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Principal Investigator |
Terai Naoki 佐賀大学, 教育学部, 教授 (90259862)
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| Co-Investigator(Kenkyū-buntansha) |
庄田 敏宏 佐賀大学, 教育学部, 准教授 (10432957)
岡田 拓三 佐賀大学, 工学(系)研究科(研究院), 准教授 (20547012)
宮崎 誓 熊本大学, 教育学部, 教授 (90229831)
青山 崇洋 佐賀大学, 教育学部, 准教授 (60516178)
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| Co-Investigator(Renkei-kenkyūsha) |
YOSHIDA KENICHI 日本大学, 文理学部, 教授 (80240802)
YANAGAWA KOUJI 関西大学, 工学部, 教授 (40283006)
KIMURA KYOUKO 静岡大学, 大学院理学研究科, 助教 (60572633)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 辺イデアル / 射影次元 / 記号的べき / Stanley-Reisnerイデアル / Stanley-Reisner イデアル / 算術階数 |
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| Outline of Final Research Achievements |
We studied the projective dimension of symbolic powers of squarefree monomial ideals in a polynomial ring. We proved that the projective dimension of the symbolic power of the edge ideal of a very well-covered graph increases with respect to the exponent. Since a well-covered bipartite graph is very well-covered and since the symbolic powers and ordinary powers coincide for the edge ideal of a bipartite graph, it implies that the projective dimension of the ordinary power of the edge ideal of a very well-covered graph increases. Moreover, we showed that the projective dimension of the symbolic power of the edge ideal of a graph with a vertex of degree one increases with respect to the exponent.
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Report
(4 results)
Research Products
(4 results)
