Grobner asymptotic expansion for regular holononic systems
Project/Area Number  10440044 
Research Category 
GrantinAid for Scientific Research (B).

Section  一般 
Research Field 
Basic analysis

Research Institution  Kobe University 
Principal Investigator 
IKEDA Hiroshi Kobe University, Faculty of Science, Professor, 理学部, 教授 (10031353)

CoInvestigator(Kenkyūbuntansha) 
TAKAYAMA Nobuki Kobe University, Faculty of Science, Professor, 理学部, 教授 (30188099)
SAITO Mutsumi Hokkaido University, Faculty of Science, Associate Professor, 理学部, 助教授 (70215565)
TAKANO Kyoichi Kobe University, Faculty of Science, Professor, 理学部, 教授 (10011678)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥4,500,000 (Direct Cost : ¥4,500,000)
Fiscal Year 1999 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1998 : ¥3,300,000 (Direct Cost : ¥3,300,000)

Keywords  Grobner deformations / Grobner basis / Monomial ideal / GKZ hypergeometric system / Asymptotic expansion / Asyonptotic expansion / Grobner diformation / GKZ hypergesmetric system / Grolner basis / Volune polynonrid / Rogular singulasity / series sohition / Standard pairs 
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.

Report
(4results)
Research Output
(12results)