A Geometric study of hypergeometric functions

超几何函数的几何研究

• 批准号: 11440050
• 负责人: YOSHIDA Masaaki
• 金额: $ 3.39万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11440050/
• 关键词: hypergeometric; twisted (co) homology; uniformization; intersection theory; hyperbolic structure; automorphic form; 刻印三次曲面; 又曲空間; テタ関数; 超幾何関数; 黒写像; 一寸来群; 無限積; 三次曲面; Schottky群; 一意化; 数論的部分群; 交点理論; 対称空間; 配置空間; 周期写像

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 involvinggot twisted Riemann inequalities absolute values in the integrands.2) Got the uniformizing differential equation of the complex hyperbolicstructure 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 determinantformulae 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 withFound 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.

我们得到以下关于超几何函数的结果。0) 研究了以格拉斯曼为模型的线性偏微分方程组。1) 研究了扭曲上同调群的 Hodge 结构，得到了许多涉及被积函数中扭曲黎曼不等式绝对值的积分公式。2) 得到了标记立方曲面模空间上复双曲结构的均匀化微分方程。证明了它是高维超几何微分方程对 d.3) 发展了扭曲循环的交集理论：得到了不一定是遗传超平面排列的行列式。在一些二次超曲面进入排列的情况下得到了部分结果。4)在标记立方曲面模空间的实轨迹上发现了双曲结构。发现对应群是双曲Coxeter群；借助模嵌入构造自同构形式。5)对超几何函数进行了几何研究，发现单向群是斯科基虚数指数。基因组2.用锉刀构建了模块化ttu。对于单一性组。

项目成果

T.Ichikawa: "On Schottky groups arising from the hypergeometric equation with imaginary exponents"Proc AMS.. 2001-9.

T.Ichikawa：“论由虚数指数超几何方程产生的肖特基群”Proc AMS.. 2001-9。

M.Yoshida: "A hyperbolic atr on the real locus of the moduli sp of marked cubic sufaces"to appear in Topology.

M.Yoshida：“标记立方面的模 sp 的实轨迹上的双曲 atr”出现在《拓扑学》中。

T.Sasaki: "Invariant theory for linear differential systems modeled after the Grassmannian Gr(n, 2n)"Nagoya J.Math.. 2001-1.

T.Sasaki：“根据格拉斯曼 Gr(n, 2n) 建模的线性微分系统的不变理论”Nagoya J.Math.. 2001-1。

T.Sasaki: "The uniformizing differential equation of the complex hyperbolic structure on the moduli space of marked cubic surfaces"Proc. Japan Acad.. 75A. 129-133 (1999)

T.Sasaki：“标记立方曲面模空间上复双曲结构的均匀化微分方程”Proc。

K.Kimachi, H.Ochiai, M.Yoshida: "Intersection theory of loaded cycles IV-resonant cases"Math. Nachr, Kyushu Univ Preprint 2002-1. (to appear).

K.Kimachi、H.Ochiai、M.Yoshida：“加载周期 IV 共振情况的交叉理论”数学。