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.

Mori等人研究了几个带缺陷的亚纯映射。他通过小变形得到了P^n（C）中亚纯映射的超曲面或有理移动目标的亏格的消去定理，并证明了在超越亚纯映射空间中无亏格的映射是稠密的。他和一位研究者Aihara还得到了对P^n（C）上任意d次超曲面，在区间（0，α）上构造了一个代数非退化的亚纯映射，其中α 0x（3E）0只依赖于d.研究者Aihara得到了代数相依的亚纯映射下因子的逆象的几个条件，并得到了依赖于亏格存在的唯一性定理.户田得到了如下结果：对于P^n（C）中在N-次一般位置上具有最大亏和的超越全纯曲线f，当N 0 x（3E）n = 2 m时，至少存在一个δ（H，f）= 1的超平面;当N 0 x（3E）n = 2 m时，至少存在N-n + 1个δ（H，f）= 1的超平面.中田调查遍历理论的行动对朱莉娅集的合理功能和行动的限制集的不连续组的莫比乌斯变换。Sekigawa得到了一个有理函数的例子，它具有一个Fatou分量，其预分配连通度n [大于或等于] 3。Kawamura发现了一个现象，即混沌结构有一个惊人的规律作为概率观点，即它具有概率密度函数的收敛性质。佐藤研究了结构的空间平移不变算子的洛伦兹空间的局部紧交换群。Mizuhara证明了哈代空间的Morrey函数和块函数的一个弱分解定理。

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）。