Commutative Ring Theory of Singularities of Algebraic Varieties
| Project/Area Number |
23540059
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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) |
YOSHIDA Ken-ichi 日本大学, 文理学部, 教授 (80240802)
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| Co-Investigator(Renkei-kenkyūsha) |
KURANO Kazuhiko 明治大学, 理工学部, 教授 (90205188)
TAKAGI Shunsuke 東京大学, 大学院・数理科学研究科, 准教授 (40380670)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 環論 / 代数学 / 特異点 / 可換環論 / 有理特異点 / 重複度 / F-threshold / F-pure rings / Hilbert-Kunz 重複度 / a 不変量 / F-pure / F-rational / jet scheme / 一般化された test ideal / 半群環 |
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| Research Abstract |
The aim of this research is to apply commutative ring theory to the study of singular points of algebraic varieties and, conversely, to express properties of commutative rings in terms of geometric language of singularities and analyze it.
Main results of this research are the followings; 1. Obtained upper bound of multiplicities of f-pure rings in terms of dimension and embedding dimension, 2. Described the quasi-socle ideals of parameter ideals using the tight closure theory of ideals of positive characteristic and got a bound, 3. Obtained the complete classification of Ulrich ideals in 2-dimensional rational singularities, 4. Characterized almost Gorenstein semigroup rings in affine 3-space in terms of its free resolution, 5. Obtained inequalities between a-invariant and F-pure threshold of homogeneous toric rings, 6. Determined when the jet schemes of a hypersurface have rational singularities.
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Report
(4 results)
Research Products
(37 results)
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[Journal Article] Ulrich ideals and modules2014
Author(s)
S. Goto, Kazuho Ozeki, , Ryo Takahashi, Kei-ichi Watanabe, Ken-ichi . Yoshida
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Journal Title
Mathematical Proceedings of the Cambridge Philosophical Society
Volume: vol.156
Pages: 137-166
Related Report
Peer Reviewed
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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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[Book] 可換環論2011
Author(s)
後藤四郎，渡辺敬一
Total Pages
350
Publisher
日本評論社
Related Report
