2010 Fiscal Year Final Research Report
Characteristic p method in singularity theory
| Project/Area Number |
20540050
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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 | Nihon University |
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Principal Investigator |
WATANABE Keichi Nihon University, 文理学部, 教授 (10087083)
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| Co-Investigator(Kenkyū-buntansha) |
TOMARI Masataka 日本大学, 文理学部, 教授 (60183878)
YOSHIDA Kennichi 名古屋大学, 多元数理研究科, 准教授 (80240802)
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| Co-Investigator(Renkei-kenkyūsha) |
FUKUDA Takuo 日本大学, 文理学部, 教授 (00009599)
KURANO Kazuhiko 明治大学, 理工学部, 教授 (90205188)
TAKAGI Shunsuke 九州大学, 大学院・理学研究科, 准教授 (40380670)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 代数学 / 特異点論 / 可換環論 / 代数幾何学 / Frobenius写像 |
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| Research Abstract |
We investigated the property of singularities appearing in the minimal model theory in algebraic geometry. Specifically, we got the following results. 1. We introduced the notion of F-thresholds of pair of ideals and got a conjecture concerning F-threshold and multiplicity of ideals. We proved the conjecture in some important cases. 2. We gave a procedure to construct (quasi) Gorenstein graded rings with given a-invariant from normal projective varieties. 3. We investigated diagonal subalgebras of multi-graded rings and gave a criterion for such rings to be rational singularity. We also gave a new example concerning theory of divisor class groups.
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[Presentation]2008
Author(s)
K.Watanabe
Organizer
Classification of 2-dimensional normal graded hypersurfaces with small a-invariants
Place of Presentation
Algebra Workshop, Kansas Univ.
Year and Date
2008-07-25
