2011 Fiscal Year Final Research Report
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(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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| Keywords | 巡回商特異点 / Cox 環 / 因子類群 / テータ不変量 / 極大 CM 加群 |
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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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