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The relation between the configuration space and the root systems

配置空间与根系统的关系

基本信息

批准号：
09640057
负责人：
SEKIGUCHI Jiro
金额：
$ 1.47万
依托单位：
Himeji Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640057/
关键词：
cross ratio variety configuration space root system 超幾何関数射影平面

项目摘要

1. (Joint work with T.Takayama (Kobe Univ.)) The system of partial differential equations for the hypergeometric function of type (3,6) lives on the configuration space of 6 points on the projective plane. We treated two kinds of compactifications of the configuration space, studied the relations between these two spaces and constructed local fundamental solutions of the system above.2. (Joint work with M.Yoshida (Kyushu Univ.)) Naruki's cross ratio variety is regarded as a compactification of the configuration space of 6 points on the projective plane. Unsig the properties of this variety, we studied the configuration space of 6 lines (= the configuration space of 6 points) on the real projective plane. In particular, we gave an interpretation of the classification of 6 lines arrangements on the real projective plane in terms of the root system of type E_6.3. I studied the relationship between the configurations of 7 lines the real projective plane and the root system of type E_7. It is known that there are mutually different 11 kinds of 7 lines arrangements on the real projective plane. I gave an interpretation of the classification in terms of the root system of type F_7.4. (Joint work with T.Fukui (Mukogawa Women's Univ.)) We studied the relationship between the configurations of 8 lines the real projective plane and the root system of type F_5. Our aim is the classification of 8 lines arrangements on the real projective plane, which is an open problem. We constructed a lot of 8 lines arrangements by a combinatorial argument.

1.（与高山先生（科比大学）合作）（3，6）型超几何函数的偏微分方程组存在于射影平面上6点的位形空间上。讨论了位形空间的两种紧化，研究了这两种紧化之间的关系，构造了系统的局部基本解.（与吉田先生（九州大学）合作）Naruki交比簇被看作是射影平面上6点位形空间的紧化。利用这一簇的性质，研究了真实的射影平面上的6条直线的位形空间（= 6点的位形空间）。特别地，我们用E_6.3型根系解释了真实的射影平面上6条直线排列的分类。研究了E_7型根系与真实的射影平面上7条直线的构形之间的关系。已知在真实的射影平面上有11种互不相同的7线排列。本文以F_7.4型根系为例，对这一分类作了解释。（与T.福井（Mukogawa女子大学）合作）本文研究了F_5型根系与真实的射影平面上8条直线的构形之间的关系。我们的目标是对真实的射影平面上的8条直线排列进行分类，这是一个公开的问题。我们通过组合论证构造了大量的8线排列。