Research on Noetherian property of symbolic Rees algebras
| Project/Area Number |
23540042
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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 | Chiba University |
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Principal Investigator |
NISHIDA Koji 千葉大学, 統合情報センター, 教授 (60228187)
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| Co-Investigator(Renkei-kenkyūsha) |
KURANO Kazuhiko 明治大学, 理工学研究科, 教授 (90205188)
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| Research Collaborator |
FUKUMURO Kosuke
INAGAWA Taro
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | 可換環 / 記号的べき乗 / 記号的リース代数 / シンボリックパワー / シンボリックリース代数 / 次数付環 / シンボリックリース環 / 代数学 / symbolic power / symbolic Rees algebra |
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| Outline of Final Research Achievements |
In this research, we aimed to find a new method for computing symbolic powers of ideals in 3-dimensional regular local (or polynomial) rings. Furthermore, we aimed to improve the Huneke's criterion for symbolic Rees algebras to be Noethrian.
In the first year, using *-transform of acyclic complexes, we found a specific procedure to induce free resolutions of symbolic powers from those of ordinary powers. Next year, we gave a new criterion on the Noetherian property of symbolic Rees algebras. In the third year, we checked the practicality of the results we found in the last two years by applying them to concrete examples. The last year was devoted for extending the class of ideals whose symbolic Rees algebras are not Noetherian.
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Report
(5 results)
Research Products
(11 results)
