2001 Fiscal Year Final Research Report Summary
A Geometric study of hypergeometric functions
| Project/Area Number |
11440050
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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 |
Basic analysis
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| Research Institution | KYUSHU UNIVERSITY |
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Principal Investigator |
YOSHIDA Masaaki Faculty of Mathematics, Professor), 大学院・数理学研究院, 教授 (30030787)
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| Co-Investigator(Kenkyū-buntansha) |
MIMACHI Katsuhisa Tokyo Inst. Of Tech. Sci & Tech. Prof., 大学院・理工学研究科, 教授 (40211594)
IWASAKI Katsunori Faculty of Math. Prof., 大学院・数理学研究院, 教授 (00176538)
SASAKI Takeshi Kobe Univ. Fac. Of Sci. Dept of Math. Prof., 理学部, 教授 (00022682)
HANAMURA Masaki Faculty of Math. Assoc. Prof., 大学院・数理学研究院, 助教授 (60189587)
MATSUMOTO Keiji Hokkaido Univ. Dept. of Math Assoc. Prof, 大学院・理学研究科, 助教授 (30229546)
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| Project Period (FY) |
1999 – 2001
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| Keywords | hypergeometric / twisted (co) homology / uniformization / intersection theory / hyperbolic structure / automorphic form |
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| Research Abstract |
We got the following results concerning hypergeometric functions.
0) Studied systems of linear partial differential equations modeled after grassmannians.
1) Investigated the Hodge structure of twisted cohomology groups and Got many integral formulae involving
got twisted Riemann inequalities absolute values in the integrands.
2) Got the uniformizing differential equation of the complex hyperbolic
structure on the moduli space of marked cubic surfaces. Proved that it is the restriction of the higher dimensional hypergeometric differential equation onto a d.
3) Developed the intersection theory for twisted cycles : got determinant
formulae for not necessarily genetic hyperplane arrangements. Got partial results in the case that some quadratic hypersurfaces get into the arrangements.
4) Found a hyperlybolic structure on the real locus of the moduli space of marked cubic surfaces. Found that the corresponding group is the hyperbolic Coxeter group ; Constructed automorphic forms by the help of a modular embedding.
5) Made a geometric study of the hypergeometric function with
Found that the monodromy groups turns out to be scottky imaginary exponents. Groups of genes 2. Constructed a modular ttu with rasp. To the monodromy group.
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