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

• 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
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640198/
• 关键词: meromorphic map; unicity theorem; algebraic dependence; Nevanlinna's deficiency; flat torus; indefinite Khaler metric; 不定値計量; 一意性定理; 代数的従属性; ネヴァンリンナ除外値; 不定値ケーラー計量

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.

主管齐哈拉（Aihara）研究了异形映射的独特问题。特别是，他给出了一个条件，即两个圆形映射成一个光滑的椭圆曲线与椭圆曲线的内态相关。他和研究人员的莫里（Mori）还构建了伴有缺陷的meromorthic映射（超出印刷的超形状映射的缺陷，预印本）。一个研究者的莫里研究了一个消除了杂态映射缺陷的问题，并获得了消除定理。研究者kitagawa studiod sutiood等速变形扁圆形液体均质浸入3个球体s^3 hi s^3具有恒定平均曲率。结果，他获得了浸入s^3中的平圆圆圆圆圆形的分类，该分类不接受等距变形。研究员卡玛达（Kamada）研究了在紧凑的复杂表面上自二个中性中性khaler量表的存在问题，并证明了一个紧凑的自动偶尔中性的khaler表面，承认某个S^1对称性是对赫尔兹布鲁克（Hirzebruch投影线。

项目成果

北川義久: "Deformable flat tori in $S^3$ with constant mean curvature"Osaka J.Math.. (印刷中).

Yoshihisa Kitakawa：“具有恒定平均曲率的 $S^3$ 中的可变形扁平环面”Osaka J.Math..（正在印刷中）。

Yoshihiro Aihara: "Algebraic dependence of meromorphic mappings in value distribution theory."to appear in Nagoya Math. J..

Yoshihiro Aihara：“值分布理论中亚纯映射的代数依赖性。”出现在名古屋数学中。

相原義弘: "Algebraic dependence of meromorphic mappings in value distribution theory"Nagoya Math.J. (印刷中).

Yoshihiro Aihara：“值分布理论中亚纯映射的代数依赖性”Nagoya Math.J（出版中）。

鎌田博行: "Indefinite analogue of hyperbolic ansatz and its application"Proc. of the Fifth Pacific Rim Geometry Conference (Sendai, 2000), 69-73, Tohoku Math. Publ.. Vol.20. 69-93 (2001)

Hiroyuki Kamata：“双曲拟形的不定类比及其应用”，第五届环太平洋几何会议论文集（仙台，2000 年），69-73，东北数学出版社，第 69-93 卷（2001 年）。

相原義弘: "Geometric conditions for uniqueness problems of meromorphic mappings"RIMS Kokyuuroku. Vol.1236. 98-111 (2001)

Yoshihiro Aihara：“亚纯映射的唯一性问题的几何条件”RIMS Kokyuuroku Vol.1236（2001）。