2000 Fiscal Year Final Research Report Summary
Variation of Hodge structures and hypergeometric functions
| Project/Area Number |
11640012
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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 | University of Tokyo |
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Principal Investigator |
TERASOMA Tomohide University of Tokyo, Departement of Mathematical Science, Associate Professor, 大学院・数理科学研究科, 助教授 (50192654)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAMATA Yujiro University of Tokyo, Departement of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (90126037)
OGUISO Keiji University of Tokyo, Departement of Mathematical Science, Associate Professor, 大学院・数理科学研究科, 助教授 (40224133)
SAITO Takeshi University of Tokyo, Departement of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (70201506)
KATSURA Toshiyuki University of Tokyo, Departement of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (40108444)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Hypergeometric functions / Toric geometry / Selberg integral / Multiple Zeta Value |
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| Research Abstract |
In the beginning of this research period, we are planning to study the relation between critical values and topological cycles for a family of toric hypersurfaces. This relateion is completely made clear. More concretely, we study them by constructing a compactification of the universal family of toric hypersurfaces in terms of convex bodies. We give an explicit comact family over the compactification of moduli associated to the secondary polytope. Using this construction, we found a correspondece between the stable cycles assciated to critical points and a formal expansion of hypergeometric functions.
Another theme of our research is on the expansion of Selberg integral with resepect to the complex exponent parameter. We obtain a complete result on this subject. We proved that the coefficient of the expansion is expressed as a linear combination of multiple zera values. The differential forms that we should consider is determined combinatorially and it happens to be equal to β-nbc base after Falk-Terao. We expect further developement in this directions.
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