1999 Fiscal Year Final Research Report Summary
Grobner asymptotic expansion for regular holononic systems
| Project/Area Number |
10440044
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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 |
Basic analysis
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| Research Institution | Kobe University |
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Principal Investigator |
IKEDA Hiroshi Kobe University, Faculty of Science, Professor, 理学部, 教授 (10031353)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Mutsumi Hokkaido University, Faculty of Science, Associate Professor, 理学部, 助教授 (70215565)
TAKAYAMA Nobuki Kobe University, Faculty of Science, Professor, 理学部, 教授 (30188099)
TAKANO Kyoichi Kobe University, Faculty of Science, Professor, 理学部, 教授 (10011678)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Grobner deformations / Grobner basis / Monomial ideal / GKZ hypergeometric system / Asymptotic expansion |
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| Research Abstract |
We establish a method to analyze asymptotic behavior of regular holonopic systems at infinity. The first order approximation is governed by the initial system. In case of GKZ hypergeometric systems, the correspondiny systems are essentially monomial ideals and hence can be analyzed by nsins combinatorial methods for them.
Our research project develops to the following new directions.
(1)Bayer and Sturmfels showed recently that monomial ideals can be studied through graph theory an stairs. Their method can be applied to study GKZ hypergeometric systems.
(2)Our method to determine asymptotic behavior will be a foundation to study the rational solutions and the global solutions. Some hypergeometric systems are special solutions of Painleve systems. There will be an exciting interaction between studies on Painleve systems and hypergeometric systems on the rational solutions, isomorphism problem and the global solutions.
(3)It is an important problem to determine the asymptotic behaviors around an irregular singular point. It, however, is still open.
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