Complex analysis of residues currents and computational algebraic analysis
| Project/Area Number |
17540150
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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 | Niigata University |
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Principal Investigator |
TAJIMA Shinichi Niigata University, Graduate School of Science and Technology, Professor (70155076)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIHARA Hisao Niigata Univ, Graduate School of Science and Technology, Professor (60114807)
KOJIMA Hideo Niigata Univ, Graduate School of Science and Technology, Associate Professor (90332824)
TAKEUCHI Kiyoshi Tsukuba Univ, Graduate School of Pure and Applied Sciences, Associate Professor (70281160)
NAKAMURA Yayoi Kinki Univ, School of Science and Engineering, Lecturer (60388494)
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| Project Period (FY) |
2005 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,630,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | multidimensional residue / holonomic D-modules / singularity / algebraic local cohomology / standard bases / homological index / Grothendiecl local duality / algorithm / ホロノミー系 / ネター作用素 / グレブナ基底 / グレブナー基底 / ホロノミック系 / 多変数留数カレント / 孤立特異点 |
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| Research Abstract |
Hypersurface isolated singularities and associated residues currents are considered in the context of algebraic analysis.
・An efficient algorithm that computes bases of a dual vector space of a Milnor algebra associated to a singular point has been constructed.
・A new method for computing standard bases of a zero-dimensional ideal in a power series ring has been proposed. The key ingredient in this approach is the concept of algebraic local cohomology and the Grothendieck local duality.
・An algorithm for construction holonomic D-modules attached to hypersurface isolated singularities has been derived and the structure of these holonomic D-modules have been investigated.
・An algorithmic method for computing homological indices of holomorphic vector fields has been proposed.
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Report
(4 results)
Research Products
(101 results)
