| Project/Area Number |
25400050
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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(Renkei-kenkyūsha) |
HASHIMOTO Mitsuyasu 岡山大学, 理学部, 教授 (10208465)
TAKAGI Shunsuke 東京大学, 数理科学研究科, 准教授 (40380670)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | Ulrich module / Ulrich ideal / rational singularity / F-threshold / McKay correspondence / Ulrich 加群 / Ulrich イデアル / 有理特異点 / 単純特異点 / Cohen-Macaulay / simple singularity / special CM module / Cohen-Macaulay ring |
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| Outline of Final Research Achievements |
I introduced the notion of Ulrich modules and Ulrich ideals as a generalization of classical Ulrich modules (or linear maximal Cohen-Macaulay modules) and developed a general theory with Shiro Goto (Meiji Univ.), Ryo Takahashi (Nagoya Univ.), Kazuho Ozeki (Yamaguchi Univ.) and Kei-ichi Watanabe (Nihon Univ.). Using special McKay correspondence, we classified a complete list of Ulrich modules and ideals over 2-dimensional rational double point. We introduced the notion of pg-ideals in terms of geometric genus, and extended an ideal theory of rational singularities. As an application, we proved an existence theorem for 2-dimensional excellent normal singularities.
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