Geometric Study of Complex Analysis

复分析的几何研究

• 批准号: 09440054
• 负责人: FUJIMOTO Hirotaka
• 金额: $ 2.18万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09440054/
• 关键词: value distribution theory; uniqueness theorems; automorphic form; algebraic group; adele geometry; isolated singularity; automorphsm group; CR-invariant; 代数的退化定理; 一意性問題; 複素線型微分方程式; ラングの予想; 正則自己同型群; アデール幾何学; ポアンカレー予想; 正則曲線の一意的定理; ア-デル幾何; C

Head investigator Fujimoto studied value-distribution-theoretic properties of meromorphic maps of C^n into P^N(C) and gave some new results as their applications.He showed that, for 3N +1 hyperplanes H_j's in P^N(C) located in general position, there exists at most two meromorphic maps f of C^n into P^N(C) such that the inverse images f^<-1>(H_j)'s, which are counted with multiplicities truncated by two, coincide with given divisors D_j's. He also proved that, for 2N +2 hyperplanes H_j, in P^N(C) located in general position, there is some positive integer l_0 such that, if two meromorphic maps f and g of C^n into P_N(C) have the same inverse images counted with multiplicities truncated by l_0 for each H_j, then f and g are algebraically degenerate.He also studied uniqueness range sets for meromorphic functions on C, namely, sets S with the property that the condition f^<-1>(S) = g^<-1>(S), counted f, g on C.For a finite set S = {a_1, a_2, ・・・, a_q}, he considers the polynomial P(w) : = (w - a_1)(w - a_2)・・・(w - a_q) and assumes that the derivative P(w) has k distinct zeros d_1, d_2, ・・・, d_h. He showed that, if k <greater than or equal> 4, q > 2k + 6, P(d_l) * P(d_m) for l * m and SIGMA_l P(d_l) * 0, then S is a uniqueness range set. He also gives some other sufficient conditions for a finite set to be a uniqueness range set.

Fujimoto研究了C^n到P^N（C）的亚纯映射的值分布理论性质，并给出了一些新的结果作为应用.他证明了：对于P^N（C）中位于一般位置的3 N +1超平面H_j，最多存在两个C^n到P^N（C）的亚纯映射f，使得重数截二后的逆像f^<-1>（H_j）与给定因子D_j重合.他还证明了，对于2N +2超平面H_j，在P^N（C）中位于一般位置，存在某个正整数l_0，使得如果C^n到P_N（C）中的两个亚纯映射f和g对每个H_j都有相同的重数截尾逆象，则f和g是代数退化的.他还研究了C上亚纯函数的唯一性值域集，即，对于<-1><-1>有限集S = {a_1，a_2，···，a_q}，他考虑多项式P（w）：=（w-a_1）（w-a_2）···（w-a_q），并假设导数P（w）有k个不同的零点d_1，d_2，···，d_h。他证明了，如果k <greater than or equal>4，q &gt; 2k + 6，P（d_l）* P（d_m）对l * m，SIGMA_l P（d_l）* 0，则S是唯一性值域集.他还给出了有限集是唯一性值域集的其他一些充分条件。

项目成果

A.Kodama: "A Characterization of certain weaboly pseudoconvex domains" Tohoku Math. J.51. (1999)

A.Kodama：“某些弱伪凸域的表征”东北数学。

J.Noguchi: "Value distribution theory of holomorphic 〓" Cnitemp. Math.222. 109-129 (1999)

J.Noguchi：“全纯的价值分布理论”Cnitemp.222（1999）。

M.Morishita: "On a fimily of subgroups of the Teichmuller modular group of genus tow obtained from the Jones representation" J.Math.Sci.Univ.Tokkyo. 4. 402-415 (1997)

M.Morishita：“关于从琼斯表示中获得的 Teichmuller 模群的子群”J.Math.Sci.Univ.Tokkyo。

Hirotaka Fujimoto: "Uniqueness problem with truncated multiplicities in value distribution theory" Nagoya Math. J.152. 131-152 (1998)

Hirotaka Fujimoto：“价值分布理论中截断多重性的唯一性问题”名古屋数学。

K.Ishizuki K.Tohge: "Hypentrans cendency of meronayhic solutions of a functional ecascation" Report.of Researhes of NIT. 27. 479-484 (1997)

K.Ishizuki K.Tohge：“功能级联的 meronayhic 解决方案的 Hypentrans cendency”NIT 研究报告。