Algebraic analysis of algebraic local cohomology and computational complex analysis of non-isolated singularities
| Project/Area Number |
21540167
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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 |
Basic analysis
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Yayoi 近畿大学, 理工学部, 准教授 (60388494)
OHARA Katsuyoshi 金沢大学, 数物科学系, 准教授 (00313635)
MATSUI Yutaka 近畿大学, 理工学部, 講師 (10510026)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 代数解析 / 局所コホモロジー / ホロノミーD-加群 / 特異点 / 対数的ベクトル場 / Tjurina数 / レゾルベント / スペクトル分解 / 並列計算 / 代数的局所コホモロジー / D-加群 / 局所b-関数 / スタンダード基底 / 最小消去多項式 / 局所b-考関数 |
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| Research Abstract |
Algebraic local cohomology classes attached to hypersurface isolated singularities are considered in the context of algebraic analysis. A new algorithm of computing parametric algebraic local cohomology classes is derived. A new framework to study logarithmic vector fields and associated holonomic D-modules is constructed. An efficient algorithm to compute spectral decomposition of square matrices is derived by analyzing resolvent.
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Report
(4 results)
Research Products
(80 results)
