2007 Fiscal Year Final Research Report Summary
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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| Keywords | multidimensional residue / holonomic D-modules / singularity / algebraic local cohomology / standard bases / homological index / Grothendiecl local duality / algorithm |
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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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[Presentation] 多変数留数2007
Author(s)
田島慎一
Organizer
第5回計算数学研究会
Place of Presentation
クロスパル新潟
Year and Date
20071000
Description
「研究成果報告書概要(和文)」より
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[Presentation] #NAME?2007
Author(s)
庄司卓夢、田島慎一
Organizer
Risa Consortium
Place of Presentation
神戸大学
Year and Date
20070300
Description
「研究成果報告書概要(和文)」より
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[Presentation] 多項式剰余公式アルゴリズム2005
Author(s)
庄司卓夢、田島慎一
Organizer
Computer Algebra
Place of Presentation
京都大学数理解析研究所
Year and Date
20051200
Description
「研究成果報告書概要(和文)」より
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[Presentation] #NAME?2005
Author(s)
田島慎一
Organizer
第48回函数論シンポジウム
Place of Presentation
鹿児島大学
Year and Date
20051000
Description
「研究成果報告書概要(和文)」より
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[Presentation] 剰余公式アルゴリズム2005
Author(s)
庄司卓夢、田島慎一
Organizer
コンピュータアルジェブラ研究の新たな発展
Place of Presentation
京都大学数理解析研究所
Year and Date
20050700
Description
「研究成果報告書概要(和文)」より
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