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Free multiarrangements and integral expressions of their derivations
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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: | 学位論文 (Theses) > 博士 （理学）
課程博士 (Doctorate by way of Advanced Course) > 理学院(Graduate School of Science)
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