2013 Fiscal Year Final Research Report
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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| Keywords | 環論 |
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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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[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
Peer Reviewed
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