Commutative Ring Theory of Singularities
| Project/Area Number |
26400053
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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 | Nihon University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
吉田 健一 日本大学, 文理学部, 教授 (80240802)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | Singularity / Local rings / surface singularity / integrally closed ideals / log resolution / rational singularity / elliptic singularity / Gorenstein ring / Local ring / integrally closed ideal / 特異点論 / 可換環論 / 有理特異点 / 整閉イデアル / 数値的半群 / イデアルの core / 特異点解消 / 特異点 / 局所環 / 整閉ｲﾃﾞｱﾙ / F-threshold / Hilbert-Kunz 重複度 / ｲﾃﾞｱﾙの core / Rees 環 / core / Ulrich イデアル / good ideal |
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| Outline of Final Research Achievements |
The singularities in algebraic geometry is described by commutative ring theory. Conversely, the geometric properties of a singularities;arity effects properties of the corresponding commutative ring and thus we can construct many examples of rings via geometric data. In this research, we focused on isolated singularities of algebraic surfaces and studies the properties of singularities by looking at integrally closed ideals of the singularity. In particular, the discovery of concept of "p_g-ideal is a big success of our research.
On the other hand, we used the method of analyzing singularities in characteristic 0 by the aid of commutative ring theory of positive characteristic, so called "F-Singularities". We could get some new properties of Hilbert-Kunz multiplicities.
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Report
(5 results)
Research Products
(22 results)
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[Journal Article] Ulrich ideals and modules2014
Author(s)
S. Goto, K. Ozeki, R. Takahashi, K. Watanabe, K. Yoshida
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Journal Title
Mathematical Proceedings of the Cambridge Philosophical Society
Volume: 156
Pages: 137-166
Related Report
Peer Reviewed
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[Presentation] F-thresholds,2015
Author(s)
K. Watanabe
Organizer
Workshop on Multiplier Ideals, Test Ideals and
Place of Presentation
Univ. Politecnica de Catalunya, Barcelona,
Year and Date
2015-09-08
Related Report
Int'l Joint Research / Invited
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[Presentation] Ulrich Ideals,2014
Author(s)
K. Watanabe
Organizer
International Meeting on numerical semigroups
Place of Presentation
Palazzone, Cortona, Italy
Year and Date
2014-09-09
Related Report
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