1998 Fiscal Year Final Research Report Summary
Study of Hyperplane Arrangements
| Project/Area Number |
09440001
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | TOKYO METROPOLITAN UNIVERSITY (1998)
Hokkaido University (1997) |
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Principal Investigator |
TAKEDA Yuichiro Tokyo Metropolitan University, Graduate School of Sciences, Assistant, 大学院・理学研究科, 助手 (30264584)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Hiroaki Tokyo Metropolitan University, Graduate School of Sciences, Associate Professor, 大学院・理学研究科, 助教授 (60217883)
KURANO Kazuhiko Tokyo Metropolitan University, Graduate School of Sciences, Associate Professor, 大学院・理学研究科, 助教授 (90205188)
URABE Tohsuke Tokyo Metropolitan University, Graduate School of Sciences, Associate Professor, 大学院・理学研究科, 助教授 (70145655)
NAKAMURA Ken Tokyo Metropolitan University, Graduate School of Sciences, Professor, 大学院・理学研究科, 教授 (80110849)
OKA Mutsuo Tokyo Metropolitan University, Graduate School of Sciences, professor, 大学院・理学研究科, 教授 (40011697)
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| Project Period (FY) |
1997 – 1998
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| Keywords | hyperplane arrangement / hypergeometric integral / local system cohomology / reflection group |
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| Research Abstract |
(1)The following result was obtained concerning hyperplane arrangements which are naturally determined by reflection groups : the modules of vector fields which are doubly tangent to the hyperplane arrangements have free bases (Solomon Terao). This result is related to an actively-studied conjective by Richard Stanley about the * arrangements. The explicit bases have been successfully described. The description is deeply related with the Saito derivation.
(2)The families of combinationally-equivalent hyperplane arrangements can degonerate in many ways. It was proved that the corresponding Gauss-Marin connections have logarithric poles. This result has been expected by specialists, but has never ben proved for arbitrary combinationally-equivalent hyperplane arrangements.
(3)The loganithmic forms with poles along reflection arrangements have been characterized by using antiinvariant differential forms (Sheplen-Terao).
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