Arrangements of hyperplanes and conics via real structures

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400060
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido University
• Principal Investigator: YOSHINAGA Masahiko 北海道大学, 理学(系)研究科(研究院), 准教授 (90467647)
• Co-Investigator(Kenkyū-buntansha): TERAO Hiroaki 北海道大学, 国際本部, 特任教授 (90119058)
• Co-Investigator(Renkei-kenkyūsha): TOKUNAGA Hiro-o 首都大学東京, 大学院理工学研究科, 教授 (30211395)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 超平面配置 / ミルナーファイバー / オイラー多項式

Outline of Final Research Achievements

We studied topological and combinatorial aspects of hyperplane arrangements. As topological aspects, we focused on Milnor fibers of hyperplane arrangements. Based on the formula describing the cohomology of Milnor fiber using real structure, we obtained certain vanishing of non-trivial monodromy.
We also studied the characteristic quasi-polynomials of Linial arrangements associated to a root system in terms of Ehrhart theory.

Free Research Field

幾何学、組合せ論