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Free multiarrangements and integral expressions of their derivations

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Please use this identifier to cite or link to this item:https://doi.org/10.14943/doctoral.k15737
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Title: Free multiarrangements and integral expressions of their derivations
Other Titles: 自由多重超平面配置とその導分の積分表示
Authors: WANG, Zixuan Browse this author
Issue Date: 25-Mar-2024
Publisher: Hokkaido University
Abstract: Given a reflection group generated by reflections, we can obtain a set of fixed subspaces of the reflections which forms a reflection arrangement. The fixed point set of each reflection is called reflecting hyperplane. In [19], they developed general theory of hyperplane arrangements. Many aspects of hyperplane arrangements, e.g. combinatorial, algebraic, and topological properties, have been studied. Studying the freeness of a central arrangement A is to consider its derivation module D(A). When D(A) is free, we say A is free. It is well known that every reflection arrangement is free. However, most arrangements are not free. On the other hand, the algebraic property of the module D(A) reflects the combinatorial property of A. Terao conjectured the free arrangement A implies the freeness of the arrangement B with the same intersection lattices. This conjecture has not been solved even in the three-dimensional case. In a word, studying freeness of arrangements is a major topic. In the process of studying free arrangements, many researchers have found that multiarrangements play an important role [30, 31, 32]. Many results applied to hyperplane arrangements are generalized to multiarrangements [6, 7]. Many researchers have studied the freeness of special multiarrangements [1, 12]. But it is quite difficult to construct an explicit basis for multiarrangements, even for two-dimensional cases [25, 27]. The doctoral thesis is inspired by the integral expressions of quasi-invariants [8, 10, 13, 15] and based on [14]. We construct the basis for certain multiarrangements by integral expressions.
Conffering University: 北海道大学
Degree Report Number: 甲第15737号
Degree Level: 博士
Degree Discipline: 理学
Examination Committee Members: (主査) 教授 齋藤 睦, 特任教授 岩﨑 克則, 准教授 松下 大介, 教授 吉永 正彦 (大阪大学・大学院理学研究科)
Degree Affiliation: 理学院(数学専攻)
Type: theses (doctoral)
URI: http://hdl.handle.net/2115/92269
Appears in Collections:課程博士 (Doctorate by way of Advanced Course) > 理学院(Graduate School of Science)
学位論文 (Theses) > 博士 (理学)

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