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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.

主要研究者相原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的传播。他给了一些标准的依赖亚纯映射从有限sheeted解析覆盖空间在复杂的m-空间到一个投影代数流形及其应用（出现在名古屋数学杂志）。特别地，他给出了一个条件，即两个到光滑椭圆曲线的全纯映射通过椭圆曲线的自同态代数相关。他和一个调查员森还提出了建设亚纯映射的不足之处（deflection的亚纯映射的超曲面，预印本）。Mori研究了亚纯映射的亏损消去问题并得到了消去定理，Kitagawa研究了等距浸入具有常平均曲率的三维球面S^3中的平坦环面的等距变形。结果，他得到了等距地浸入S^3中的不允许等距变形的平坦环面的分类。Kamada研究了紧致复曲面上自对偶中立型Khaler度量的存在性问题，证明了一个具有一定S^1对称性的紧致自对偶中立型Khaler曲面与秩d [小于或等于] 2的Hirzebruch曲面之一是双全纯的。他还研究了建设明确的自我双重中立的哈勒度量的产品复杂的投影线。