Study of local rings with discrete class group and its Picard number
| Project/Area Number |
21540050
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Meiji University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
早坂 太 明治大学, 理工学部, 講師 (20409460)
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| Co-Investigator(Renkei-kenkyūsha) |
KAMOI Yuji 明治大学, 商学部, 講師 (80308064)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 巡回商特異点 / Cox 環 / 因子類群 / テータ不変量 / 極大 CM 加群 / Cox環 / 極大CM加群 / 標準加群 / 有限生成性 / 永田予想 / regularity / Seshadri constant / ピカール群 / チャウ群 / 数値的同値 / 局所環 |
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| Research Abstract |
We proved that a Gorenstein isolated quotient singularity of odd prime dimension is a cyclic quotient singularity. We proved that the theta pairing defined by Hochster gives a pairing over the Grothendieck group divided by numerical equivalence. As a consequence, we proved that the class group of three dimensional isolated hypersurface singularity is torsion-free, and there always exists a counterexample of Dutta-Hochster-MacLauglin type if it is not a UFD.
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Report
(4 results)
Research Products
(43 results)
