Analysis of special functions associated with periods of algebraic varieties

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400033
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: Matsumoto Keiji 北海道大学, 理学(系)研究科(研究院), 教授 (30229546)
• Co-Investigator(Renkei-kenkyūsha): OHARA Katsuyoshi 金沢大学, 数物科学系, 准教授 (00313635) ; TERASOMA Tomohide 東京大学, 数理科学研究科, 教授 (50192654) ; YOSHIDA Masaaki 九州大学, 名誉教授 (30030787)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 超幾何関数 / 超幾何微分方程式 / 局所系係数ホモロジー群 / 局所系係数コホモロジー群 / 交点形式 / モノドロミー表現 / 接続行列

Outline of Final Research Achievements

Period integrals of algebraic varieties can be regarded as hypergeometric functions, and they satisfy a system of linear differential equations so that
a vector space of its local solutions (a local solution space) is finite dimensional. For some of such systems, I characterize the monodromy representation which describe a global property of a map defined by a basis of its local solution space, and the connection matrix of the first order differential equation with a vector-valued unknown function equivalent to the original system. In this study, I make clear their structures by using the intersection forms defined between twisted (co)homology groups which are induced from period integrals.

Free Research Field

特殊関数論