| Project/Area Number |
22540047
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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 | Nihon University (2012)
Nagoya University (2010-2011) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
HASHIMOTO Mitsuyasu 名古屋大学, 大学院・多元数理科学研究科, 准教授 (10208465)
IYAMA Osamu 名古屋大学, 大学院・多元数理科学研究科, 教授 (70347532)
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| Co-Investigator(Renkei-kenkyūsha) |
TERAI Naoki 佐賀大学, 文化教育学部, 教授 (90259862)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 環論 / Hilbert-Kunz 重複度 / テストイデアル / コーエン・マコーレー性 / Ｆ閾値 / Ｆ純閾値 / 単項式イデアル / 辺イデアル / トーリック環 / 乗数イデアル / エッジイデアル / コーエンマコーレー環 / 完全交叉 / 正則環 |
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| Research Abstract |
We give a calculation method of the diagonal F-thresholds on binomial hypersurfaces. Moreover, we prove an inequality on the diagonal F-thresholds, the a-invariant (due to Goto and Watanabe) and the F-pure thresholds on standard graded affine toric rings. We discuss Cohen-Macaulay properties of powers of edge ideals of simple graphs, and characterize graphs higher powers of edge ideals for which are Cohen-Macaulay. Furthermore, we give a similar result in the case of second power. As an application of Skoda's theorem, we prove a variant of Wang's theorem (about Goto number).
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