Value distribution thieory of meromorphic mappings, in particular, uniqueness, degeneracy and normal families of meromorphic mappings

亚态映射的值分布理论，特别是亚态映射的唯一性、简并性和正态族

基本信息

批准号：
12640198
负责人：
AIHARA Yoshihiro
金额：
$ 1.98万
依托单位：
Numazu College of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

The head investigator Aihara has studied the uniqueness problem of meromorphic mappings.He has investigated the propagation of algebraic dependence of meromorphic mappings. He gave some criteria for dependence of meromorphic mappings from finite sheeted analytic covering spaces over the complex m-space into a projective algebraic manifold and their applications (to appear hi Nagoya Math. J.). In particular, he gave a condition that two holomorphic mappings into a smooth elliptic curve are algebraically related by endomorphisms of elliptic curve. He and a investigator Mori also gave a construction of meromorphic mappings with deficiencies (Deficiencies of meromorphic mappings of hypersurfaces, preprint). An investigator Mori studied an elimination problem of defects of meromorphic mappings and obtained elimination theorems.An investigator Kitagawa studied isometric deformations of flat tori isometrically immersed hi the 3-sphere S^3 with constant mean curvature. As a result, he obtained a classification of the flat tori isometrically immersed in S^3 which admit no isometric deformation. An investigator Kamada studied the existence problem for self-dual neutral Khaler metrics on compact complex surfaces, and proved that a compact self-dual neutral Khaler surface admitting a certain S^1 symmetry is biholomorphic to one of the Hirzebruch surfaces of rank d 【less than or equal】 2. He also studied a construction of explicit self-dual neutral Khaler metrics on the product of complex projective lines.

首席研究员 Aihara 研究了亚纯映射的唯一性问题。他研究了亚纯映射的代数依赖性的传播，他给出了亚纯映射从复杂 m 空间上的有限片解析覆盖空间到射影代数的依赖性的一些标准。流形及其应用（出现在名古屋数学杂志上）特别是，他给出了两个全纯映射成光滑的条件。椭圆曲线与椭圆曲线的自同态在代数上相关。他和研究者 Mori 还给出了一种具有缺陷的亚纯映射的构造（Defiicicies of meromorphic mappings of hypersurfaces，预印本）。消除定理。北川研究员研究了等距浸没在 3 球体中的平面环面的等距变形具有恒定平均曲率的 S^3 结果，他获得了等距浸没在 S^3 中的平面环面的分类，该分类不允许等距变形。 Kamada 研究了紧凑复杂曲面上自对偶中性 Khaler 度量的存在问题。，并证明了承认一定 S^1 对称性的紧致自对偶中性 Khaler 曲面对于秩 d 【小于或等于】2 的 Hirzebruch 曲面之一是双全纯的。He还研究了复杂射影线乘积的显式自对偶中性 Khaler 度量的构造。