| Project/Area Number |
13440015
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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 | Nihon University |
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Principal Investigator |
WATANABE Keiichi Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (10087083)
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| Co-Investigator(Kenkyū-buntansha) |
TOMARI Masataka Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (60183878)
FUKUDA Takuo Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (00009599)
MOTEGI Kamahi Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (40219978)
KURANO Kazuhiko Meiji University, School of Science and Technology, Professor, 理工学部, 教授 (90205188)
HARA Nobuo Tohoku University, Graduate School of Science, Assistant Lecturer, 大学院・理学研究科, 助教授 (90298167)
鈴木 正彦 日本大学, 文理学部, 教授 (00171249)
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| Project Period (FY) |
2001 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥7,100,000 (Direct Cost: ¥7,100,000)
Fiscal Year 2004: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2003: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2002: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2001: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | multiplier ideal / lc threshold / F-pure / Hilbert-Kunz multiplicity / Frobenius endomorphism / log terminal singularity / tight closure / regular local ring / F-pure threshold / 整閉イデアル / log resolution / UFD / Seifelt手術 / Chow群 / 特異点 / 可換環論 / 全座標環 / Hilbert-Kunz重複度 / 素元分解環 / 特異点の解消 / tight closure / 有理特異点 / subadditivity / regular ring / F-regular ring / terminal singularity / blowing up / 商特異点 / F-pure ring |
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| Research Abstract |
The results are mainly concerning the followings 3 themes
1.Multiplier ideals ;
J.Lipman and K.Watanabe proved that every integrally closed ideal in 2 dimensional regular local rings is a multiplier ideal.
N.Hara and K.Yoshida defined a generalization of "tight closures" in characteristic p>0 and by using that concept, they Succeeded to calculate multiplier ideals by purely algebraic (by commutative ring theory) method.
S.Takagi and K.Watanabe established the notion of "F-pure thresholds", which corresponds to the notion of lc(=log canonical) threshold in characteristic 0, used in algebraic geometry. This concept has many interesting features in both singularity theory and commutative ring theory.
2.Hilbert-Kunz multiplicity ;
Hilbert-Kunz multiplicity is a kind of multiplicity defined for rings of positive characteristics. Watanabe and Yoshida proved before that a ring is regular if and only if the HK multiplicity of the ring is 1. This time we determined the rings whose HK multiplicity is smallest among non-regular rings in dimension 2 and 3.
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