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Geometric researches in complex analysis

复杂分析中的几何研究

基本信息

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

项目摘要

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.

本研究的目的是从几何的角度探讨复分析，并给出复分析在几何中的应用。为此，我们需要在数学的各个领域的研究人员进行交流。我们在这些领域中多次获得了各种各样的渐近性，并得到了许多新的结果。藤本成功地在n（大于或等于3）维复射影空间中构造了2^n次双曲超曲面。他还得到了多项式是唯一多项式的一些充分条件。S. Mori和Y. Aihara等构造了复射影空间中具有预赋正亏的全纯映射的许多例子。T.上田研究了C^n中多项式自同构的不动点，证明了在一定条件下广义Henon映射的全纯Lefshetz指标之和为零.通过引入平衡矢量势的概念，H.山口阐明了和声形式的重要性。H.佐藤创立了许多类型的约根森团体。H. Kazama研究了一维复环面上拓扑平凡线丛的复解析上同调群，证明了与线丛相关的形式Hartogs-Laurent级数的存在性。A.儿玉研究了边界是强伪凸的域的条件，排除了一些奇点，成为关于韦伯斯特矩阵的完备黎曼流形。