Study on polynomial maps and hypergeometric functions of several variables
| 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 |
|
|---|
| 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
|
| Project Status |
Completed (Fiscal Year 2015)
|
| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
|---|
| 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 / 代数解析学 |
|---|
| 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.
|
Report
(4 results)
Research Products
(19 results)
