2001 Fiscal Year Final Research Report Summary
Research on arrangements of hyperplanes
| Project/Area Number |
11440012
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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 Univ. |
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Principal Investigator |
TERAO Hiroaki Tokyo Metropolitan Univ., Department of Math., Professor, 理学研究科, 教授 (90119058)
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| Co-Investigator(Kenkyū-buntansha) |
TOKUNAGA Hiroo Tokyo Metropolitan Univ., Department of Math., Assistant Professor, 理学研究科, 助教授 (30211395)
KAWASAKI Takeshi Tokyo Metropolitan Univ., Department of Math., Assistant, 理学研究科, 助手 (40301410)
OKA Mutsuo Tokyo Metropolitan Univ., Department of Math., Professor, 理学研究科, 教授 (40011697)
NAKAMURA Ken Tokyo Metropolitan Univ., Department of Math., Professor, 理学研究科, 教授 (80110849)
NAKASHIMA Tooru Tokyo Metropolitan Univ., Department of Math., Assistant Professor, 理学研究科, 助教授 (20244410)
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| Project Period (FY) |
1999 – 2001
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| Keywords | hyperplane arrangement / hyper geometric integral / local system cohomology / reflection group |
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| Research Abstract |
In the 2001 fiscal year, we obtained the following two major research results :
1. We showed that there exists a canonical basis for the module of vector fields tangent to a Coveter arrangement in a multiple order. We also showed the basis has deep relations with the flat structure of the orbit space.
2. We determined the structure of the differential module generated by reciprocals of linear forms. In particular, we obtained a formula for its Poincare series (to appear in J. Algebra).
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