| Project/Area Number |
11640015
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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 | TOKYO INSTITUTE OF TECHNOLOGY |
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Principal Investigator |
KUROKAWA Nobushige (2000) Graduate School of Science and Engineering TOKYO INSTITUTE OF TECHNOLOGY, Professor, 大学院・理工学研究科, 教授 (70114866)
石井 志保子 (1999) 東京工業大学, 大学院・理工学研究科・数学専攻, 教授 (60202933)
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| Co-Investigator(Kenkyū-buntansha) |
MIZUMOTO Shinichiro Graduate School of Science and Engineering TOKYO INSTITUTE OF TECHNOLOGY, Assistant Professor, 大学院・理工学研究科, 教授 (90166033)
TSUJI Hajime Graduate School of Science and Engineering TOKYO INSTITUTE OF TECHNOLOGY, Assistant Professor, 大学院・理工学研究科, 助教授 (30172000)
FUJITA Takao Graduate School of Science and Engineering TOKYO INSTITUTE OF TECHNOLOGY, Professor, 大学院・理工学研究科, 教授 (40092324)
黒川 信重 東京工業大学, 大学院・理工学研究科, 教授 (70114866)
斎藤 秀司 東京工業大学, 大学院・理工学研究科, 教授 (50153804)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2000: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1999: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | Zeta function / log-canonical singularity / index of singularity / exceptional singularity / modular L-function / Singularities / toric variety / index / Zariski decomposition / birational geometry |
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| Research Abstract |
We gave an estimation of the multiplicity of the principal series. We obtained basic properties of the spectra of categories and studied examples.
It was proved by Chen-Ishii that the set of the values of -K^2 for normal surface singularities has no accumulation points from above and has many accumulation points from below. We checked the closedness of this set in the real number field. The closedness is equivalent to the fact that every accumulation point is a value of -K^2 of a singular point. We proved that every accumulation point is the sum of finite number of the value of -K^2.
And non-closedness of the set was proved.
We proved the boundedness of the indices of isolated strictly log-canonical singularities of dimension 3 and also obtained all possible values of the indices.
We constructed counter examples of Reid's conjecture : hypersurface rational singularities are characterized by weights. As one of the consequences, we obtained simple K3 singularities which is not in the category of simple K3 singularities of famous 95 types.
We proved that for every hypersurface canonical singularity defined by a non-degenerate function there is a weight such that the singularity defined by the leading tern with respect to this weight is exceptional if and only if the original singularity is exceptional. So we can reduce the problem of exceptionality of the singularity into the weighted homogeneous case. We also proved that the number of the weights whose singularities are exceptional is finite.
We studied the order of zeros at the center of equations of modular L-functions. In particular we studied Rankin zta function corresponding to the pair of elliptic modular forms.
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