Research of multiplier ideals and tight closures from viewpoint of commutative algebra and computational algebra
| Project/Area Number |
19340005
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Nagoya University |
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Principal Investigator |
YOSHIDA Ken-ichi Nagoya University, 大学院・多元数理科学研究科, 准教授 (80240802)
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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)
FUJINO Osamu 名古屋大学, 大学院・多元数理科学研究科, 准教授 (60324711)
寺井 直樹 佐賀大学, 文化教育学部, 准教授 (90259862)
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| Co-Investigator(Renkei-kenkyūsha) |
TERAI Naoki 佐賀大学, 文化教育学部, 准教授 (90259862)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥8,450,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,950,000)
Fiscal Year 2009: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2008: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2007: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
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| Keywords | 乗数イデアル / 密着閉包 / F正則性 / 正則局所環 / コーエン・マコーレー性 / スタンレー・リースナー環 / グラフ / 算術的階数 / テストイデアル / エッジイデアル / 完全交叉 / マコーレー性 / スタンレー・リースナーイデアル / Hilbert-Kunz重複度 / グラフイデアル / Stanley-Reisner環 / 形式的冪 / Buchsbaum環 / 判定イデアル / 特異点 / 局所化 / 完備化 |
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| Research Abstract |
The leader of this research introduced the notion of a generalized tight closure and succeeded to redefine multiplier ideals in terms of commutative ring theory. Precisely speaking, the multiplier ideal is given as the limit of generalized test ideals. In this research, we found several differences between the behavior of test ideals and that of multiplier ideals. Moreover, we extended the theory of test ideals in order to study several invariants in the theory of commutative algebra.
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Report
(4 results)
Research Products
(56 results)
