Singularities on algebraic varieties
Project/Area Number |
22340004
|
Research Category |
Grant-in-Aid for Scientific Research (B)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
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Research Institution | The University of Tokyo |
Principal Investigator |
ISHII Shihoko 東京大学, 数理(科)学研究科(研究院), 教授 (60202933)
|
Co-Investigator(Kenkyū-buntansha) |
WATANABE Keiichi 日本大学, 文理学部, 教授 (10087083)
TAKAGI Shunsuke 東京大学, 大学院数理科学研究科, 准教授 (40380670)
TOMARU Tadashi 群馬大学, 医学部, 教授 (70132579)
|
Project Period (FY) |
2010-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥17,420,000 (Direct Cost: ¥13,400,000、Indirect Cost: ¥4,020,000)
Fiscal Year 2013: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2012: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2010: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
|
Keywords | 特異点 / 弧空間 / 極小対数的食い違い数 / singularities / jet scheme / ジェットスキーム / 食い違い数 / discrepancy / Frobenius 射 / arc space / rational singularity / log-canonical singularity / multiplier ideal / graded ring |
Outline of Final Research Achievements |
We proved the Inversion of Adjunction formula according to the minimal log discrepancies which is defined by Mather-Jacobian discrepancies. By means of this discrepancies we introduced MJ-canonical singularities and also MJ-multiplier ideal. We also prove that the ideal has good properties; vanishing theorem, subaddidivity property and so on. In general MJ-minimal log discrepancy is greater than of equal to the dimension of the variety, we determined all MJ , we determined singularities whose MJ-minimal log discrepancy.
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Report
(5 results)
Research Products
(58 results)
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[Presentation] 特異点の問題2010
Author(s)
S.Ishii
Organizer
複素幾何学の諸問題
Place of Presentation
京都大学数理解析研究所
Year and Date
2010-09-07
Related Report
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[Presentation] Some topics on F-thresholds2010
Author(s)
K.Watanabe
Organizer
Frobenius splitting in algebraic geometry, commutative algebra, and representation theory
Place of Presentation
University of Michigan (USA)
Year and Date
2010-05-18
Related Report
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[Presentation] Introduction to F-singularities2010
Author(s)
S.Takagi
Organizer
Frobenius splitting in algebraic geometry, commutative algebra, and representation theory
Place of Presentation
University of Michigan (USA)
Year and Date
2010-05-17
Related Report
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