Minimal free resolutions and the arithmetical rank of Stanley-Reisner ideals
| Project/Area Number |
23540053
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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, 文化教育学部, 教授 (90259862)
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| Co-Investigator(Kenkyū-buntansha) |
UEHARA Tsuyoshi 佐賀大学, 工学系研究科, 教授 (80093970)
ICHIKAWA Takashi 佐賀大学, 工学系研究科, 教授 (20201923)
MIYAZAKI Chikashi 佐賀大学, 工学系研究科, 教授 (90229831)
KAWAI Shigeo 佐賀大学, 文化教育学部, 教授 (30186043)
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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, 准教授 (40283006)
KIMURA Kyouko 静岡大学, 大学院・理学研究科, 助教 (60572633)
MURAI Satoshi 山口大学, 理学部, 講師 (90570804)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | Stanley-Reisner ideal / minimal free resolution / arithmetical rank / Stanley-Reisner イデアル / 算術階数 / 極小自由分解 / Ｓｔａｎｌｅｙ－Ｒｅｉｓｎｅｒ イデアル |
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| Research Abstract |
We studied the arithmetical rank of Stanly-Reisner ideals, which are squarefree monomial ideals in a polynomial ring. It is known that the arithmetical rank of a Stanley-Reisner ideal is greater than or equal to the projective dimension of the Stanley-Reisner ring, which is the length of the minimal free resolutions of the quotient ring. As for the edge ideal of a forest, Barile conjectures that these numbers will be coincident. We proved it. As for a Gorenstein Stanly-Reisner ideal of height three, we proved that its arithmetical rank is equal to the projective dimension of the Stanly-Reisner ring, too.
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Report
(4 results)
Research Products
(27 results)
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[Presentation] Licci squarefree monomial ideals2013
Author(s)
寺井直樹
Organizer
International conference on commutative algebra and its interaction to algebraic geometry and combimatorics
Place of Presentation
Vitetnam Institute for Advanced Study in Mathematics, Hanoi
Year and Date
2013-12-09
Related Report
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