Grobner asymptotic expansion for regular holononic systems

正则完整子系统的 Grobner 渐近展开式

• 批准号: 10440044
• 负责人: IKEDA Hiroshi
• 金额: $ 2.88万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10440044/
• 关键词: Grobner deformations; Grobner basis; Monomial ideal; GKZ hypergeometric system; Asymptotic expansion; Grobner diformation; Asymptotic expansion; GKZ hypergesmetric system; Grolner basis; Volune polynonrid; Rogular singulasity; series sohition /

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.

我们建立了一种分析无穷远正则全息系统渐近行为的方法。一阶近似由初始系统控制。对于GKZ超几何系统，相应的系统本质上是单项式理想，因此可以通过nsins组合方法对其进行分析。我们的研究项目向以下新方向发展。（1）Bayer和Sturmfels最近表明单项式理想可以通过图论和阶梯来研究。他们的方法可以应用于研究GKZ超几何系统。(2)我们确定渐近行为的方法将为研究有理解和全局解奠定基础。一些超几何系统是 Painleve 系统的特殊解。 Painleve系统和超几何系统的有理解、同构问题和全局解的研究将会产生令人兴奋的互动。(3)确定不规则奇点周围的渐近行为是一个重要的问题。然而，它仍然开放。

项目成果

Matsumi Saito: "Hypergeometric Polynomials and Integer Programming"Composition Mathematics. 115. 185-204 (1995)

Matsumi Saito：《超几何多项式和整数规划》组合数学。

Mutsumi Saito: "Hypergeonotric Polynomials and Integer Programming"Composition Mathematics. 115. 185-204 (1999)

Mutsumi Saito：“超几何多项式和整数规划”复合数学。

M.Saito, B.Sturnfelds, N.Takayama: "Grobner deformations of hypergeometric differential equations"Springer. (1999)

M.Saito、B.Sturnfelds、N.Takayama：“超几何微分方程的格罗布纳变形”施普林格。