Geometric researches in complex analysis

复杂分析中的几何研究

• 批准号: 12304007
• 负责人: FUJIMOTO Hirotaka
• 金额: $ 16.99万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12304007/
• 关键词: hyperbolic manifold; value distribution theory; holomorphic mapping; uniqueness theorem; defect; holomorphic automorphism group; complex dynamics; complex differential equation; 一意性多項式; 双曲型多様体; 多項式自己同型写像; 正則レフシェッツ指数; 正則曲線; 一般複素楕円形; 理想境界; ヨル

The purpose of this research is to investigate complex analysis in the aspect of geometry and, moreover, to give applications of complex analysis to geometry. To these ends, we need to have interchanges of researchers in various fields of mathematics. We held various sympsiums many times and obtained many new results in these fields.H. Fujimoto succeeded in the constructions of hyperbolic hypersurfaces of degree 2^n in the n (【greater than or equal】3)-dimensional complex projective space. He also obtained some sufficient conditions for polynomials to be uniqueness polynomials. S. Mori, together with Y. Aihara, constructed many examples of holomorphic mappings into the complex projective space with pre-assinged positive deficiency. T. Ueda studied fixed points of polynomial automorphisms of C^n and showed that the sum of holomorphic Lefshetz indices vanishes for generalized Henon maps under some conditions. By introducing the notion of balayage vector potentials, H. Yamaguchi maked clear the importance of harmonic forms. H. Sato founded many kinds of Jorgensen groups. H. Kazama studied complex analytic cohomology groups of topologically trivial line bundles over 1-dimension complex torus and showed the existence of formal Hartogs-Laurent series associated with line bundles. A. Kodama investigated the conditions for domains whose boundary are strongly pseudo-convex excluding some singularities to become complete Riemannian manifolds with respect to Webster me trices.

这项研究的目的是研究几何方面的复分析，此外，为了实现复分析在几何中的应用，我们需要在数学的各个领域进行交流。 H.藤本成功地构造了n（大于或等于）3维复射影空间中的2^n次双曲超曲面。多项式S. Mori 与 Y. Aihara 一起构建了许多具有预置正缺陷的复射影空间的全纯映射示例。T. Ueda 研究了 C^n 的多项式自同构的不动点，并表明在某些条件下，广义 Henon 映射的全纯 Lefshetz 指数之和消失 通过引入 balayage 矢量势的概念，H. Yamaguchi 明确了其重要性。 H. Sato 建立了多种 Jorgensen 群，研究了一维复环上的拓扑平凡线束的复解析上同调群，并证明了与线束 A 相关的形式 Hartogs-Laurent 级数的存在。 Kodama 研究了边界为强伪凸的域（排除某些奇点）成为关于韦氏矩阵的完全黎曼流形的条件。

项目成果

M.Shirosaki: "A family of polynomials with the uniqueness poperty for linearly nondeger be hlomoyhic mapings"Kodai Mathematical Journal. 25. 288-292 (2002)

M.Shirosaki：“具有线性非德格同调映射的唯一性的多项式族”Kodai Mathematical Journal。

Hiroki Satoh: "Jorgensen's inequality for classical Schottky groups of real type, II"Journal of Mathematical Society of Japan. 53. 791-811 (2001)

Hiroki Satoh：“实型经典肖特基群的乔根森不等式，II”日本数学会杂志。

Seiki Mori: "Defects of holomorphic curves into P^n(C) for rational moving targets and a space of meromorphic mappings"Complex Variables. 43. 363-379 (2001)

Seiki Mori：“有理移动目标的全纯曲线到 P^n(C) 的缺陷和亚纯映射空间”复杂变量。

Akio Kodama: "A remark on generalized complex ellipsoids with spherical boundary points"Korean Math. J.. 51. 285-295 (2000)

Akio Kodama：“关于具有球形边界点的广义复杂椭球体的评论”韩国数学。

H.Kazama and S.Takayama: "On the 〓-eqation over pseudoconvex Kahler manifolds"Manuscripta Math.. 102. 25-39 (2000)

H. Kazama 和 S. Takayama：“论伪凸卡勒流形上的〓方程” Manuscripta Math.. 102. 25-39 (2000)