Groebner Bases for Systems of Multivariable Hypergeometric Differential Equations

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17592
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tokai University
• Principal Investigator: Nakayama Hiromasa 東海大学, 理学部, 講師 (00595952)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: グレブナー基底 / 超幾何関数 / 超幾何微分方程式

Outline of Final Research Achievements

To execute algorithms in D-modules, we need to obtain Groebner bases for ideals in the ring of differential operators. We have algorithms to compute Groebner bases, but for systems of differential equations including many variables or n variables, we cannot execute the algorithms.
In this research, we theoretically compute Groebner bases for systems of multivariable hypergeometric differential equations without computer. By using these Groebner bases we derive characteristic varieties, singular locus and Pfaffian systems for systems of multivariable hypergeometric differential eqautions.

Free Research Field

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