RESEARCH OF A SPACE OF MEROMORPHIC MAPPINGS AND DEFICIENCIES

亚形映射空间和缺陷的研究

• 批准号: 12640150
• 负责人: MORI Seiki
• 金额: $ 2.24万
• 依托单位: Yamagata University
• 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 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640150/
• 关键词: value distribution theory; meromorphic mapping; defect; unicity theorem; function space; complex dynamical system; dynamical system for chaos; Julia set; 有利形写像; ネヴァンリナ理論; 有理型写像; 値分布論; 測度空間; 力学系; 射影空間; モーリー空間; ウエヴレット理論; 楕円曲線

The head investigator Mori-researched a fewness of meromorphic mappings with defects. He obtained elimination theorems of defects of hypersurfaces or rational moving targets of a meromorphic mapping into P^n(C) by a small deformation, and he also proved that mappings without defects are dense in a space of transcendental meromorphic mappings He and an investigator Aihara also obtained results that for any hypersurface of degree d on P^n(C), we can construct an algebraically nondegenerate meromorphic mapping with a preassaigned deficiency in an interval (0,α), where α 0x(3E) 0 depends only on d. An investigator Aihara obtained serveral conditions on the inverse image of a divisor under meromorphic mappings for which mappings are algebraically dependent, and he also obtained uniqueness theorems depending on the existance of defects. Toda obtained results that for a transcendental holomorphic curve f with maximaldeficiency sum in N-subgeneral position in P^n(C), there exists at least one hyperplane with δ(H, f) = 1 if N 0x(3E) n = 2m, and also exists at least N - n + 1 hyperplanes with δ(H, f) = 1 if N 0x(3E) n. Nakada investigated the ergodic theory of actions on the Julia set of a rational function and actions on the limit set of a discontinuous group of Mobius transformations. Sekigawa obtained an example of a rational function which has a Fatou component with preassinged connectivity n 【greater than or equal】 3. Kawamura found a phenomenon that a chaostic structure has a striking rule as a probablistic view point, that is, it has a convergence property of a probabilitistic density function. Sato studied the structure of the space of translation invariant operators on a Lorentz space of locally compact abelian groups. Mizuhara proved a weak decomposition theorem of Morrey functions and block functions of the Hardy space.

首席调查员莫里（Mori）研究了少数有缺陷的meromorthic映射。他通过较小的变形得出了脱甲虫缺陷或合理移动目标的消除定理，他还证明，没有缺陷的映射，没有缺陷的映射是在超验Mappings的一个超确定映射的空间中密集的，他和研究员的构造均可构建。代数非排定的非形态映射，在间隔（0，α）中具有预先宣称的缺陷，其中α0x（3E）0仅取决于d。研究者AIHARA在Meromorormorphic映射下获得了映射的分裂的逆图，其映射的代数依赖性依赖，他还根据缺陷的存在，获得了唯一的定理。 TODA获得的结果是，对于在p^n（c）中具有最大降压性总和的跨验全态曲线f，如果n = 2m n = 2m，则至少存在一个超平面，至少存在δ（h，f）= 1，并且至少存在n -n -n -n + 1超pllanes and n -n + 1超pllanes aflyplanes aflyplanes aflyplanes n n = n n = n n n = n n n = n n n = n n n = n n = n n = 1（h，f）。中田调查了对朱莉娅（Julia）集合的行动理论的理性函数和行动对不连续的莫比乌斯转换群体的极限集的作用。 Sekigawa获得了一个有理函数的示例，该函数具有具有较愉快的连通性n [大于或相等]的FATOU组件3。Kawamura发现了一种现象，即ChaoStic结构具有引人注目的规则作为问题观点，也就是说，它具有概率密度函数的收敛性能。佐藤研究了翻译空间不变式操作员在本地紧凑的阿贝尔群体的洛伦兹空间上的结构。瑞马拉（Mizuhara）证明了莫雷（Morrey）函数的弱分解定理和耐力空间的堵塞函数。

项目成果

TODA Nobushige: "On the deficiency of holomorphic curves with maximal deficiency sum"Kodai Mathematical Journ.. 24-1. 134-146 (2001)

户田信重：“论具有最大缺值和的全纯曲线的缺项”Kodai Mathematical Journal.. 24-1。

Aihara Y.: "Propagation of algebraic dependence of meromorphic mappings"Taiwanese Journal of Mathematics. Vol.5(3). 667-679 (2001)

Aihara Y.：“亚纯映射的代数依赖性的传播”台湾数学杂志。

MORI Seiki: "Defects of holomorphic curves into P^n(C) for rational moving targets and a space of meromorphic mappings"Complex Variables Theory and Applications. Vol. 43-4. 363-379 (2001)

森精机：“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”复杂变量理论与应用。

HATORI Osamu and SATO Enji: "Decompositions of measures on compact abelian groups"Tokyo Journ. of Mathematics. Vol. 24-1. 13-18 (2001)

HATORI Osamu 和 SATO Enji：“紧阿贝尔群测度的分解”东京日报。

AIHARA Yoshihiro, MORI Seiki: "A construction of meromorphic mappings with deficiencies."Korean Journ. of Mathematics. (印刷中)(to appear).

AIHARA Yoshihiro，MORI Seiki：“存在缺陷的亚态映射的构造”。《韩国数学杂志》（正在出版）（待发表）。