Study on polynomial maps and hypergeometric functions of several variables

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400104
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: University of Tsukuba
• Principal Investigator: Takeuchi Kiyoshi 筑波大学, 数理物質系, 教授 (70281160)
• Co-Investigator(Renkei-kenkyūsha): MATSUI Yutaka 近畿大学, 理工学部, 准教授 (10510026)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: D-加群 / 超幾何関数 / 特異点理論 / モノドロミー / 偏屈層 / ミルナー束

Outline of Final Research Achievements

We studied monodromies at infinity of polynomial maps. Especially for the maps which are not tame at infinity, by proving a vanishing theorem on the cohomology groups of generic fibers, we described the Jordan normal forms of their monodromies at infinity in many cases. As a byproduct of this study, we obtained also a description of the bifurcation sets of polynomial maps. Moreover, a formula for the characteristic polynomials of the monodromies at infinity of confluent A-hypergeometric functions was obtained. As for the monodromy conjecture, we confirmed it for polynomials which are non-degenerate at the origin in many cases.

Free Research Field

代数解析