1998 Fiscal Year Final Research Report Summary
The relation between the configuration space and the root systems
| Project/Area Number |
09640057
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Himeji Institute of Technology |
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Principal Investigator |
SEKIGUCHI Jiro Faculty of Science Material Science, Himeji Institute of Technology, Professor, 理学部, 教授 (30117717)
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| Project Period (FY) |
1997 – 1998
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| Keywords | cross ratio variety / configuration space / root system / 超幾何関数 |
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| Research Abstract |
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.
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