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.

首席研究员 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其应用。他表明，对于 P^N(C) 中的 3N +1 超平面 H_j位于一般位置，最多存在两个 C^n 到 P^N(C) 的亚纯映射 f，使得逆像 f^<-1>(H_j)'s 计算为重数被截断为 2，与给定除数 D_j 一致 他还证明，对于 2N +2 个超平面 H_j，在位于一般位置的 P^N(C) 中，存在某个正整数 l_0，使得如果两个亚纯映射 f 和将 C^n 的 g 转化为 P_N(C) 具有相同的逆像，对于每个 H_j，用 l_0 截断重数进行计数，则 f 和 g 为他还研究了C上亚纯函数的唯一性范围集，即集合S，具有满足条件f^<-1>(S) = g^<-1>(S)的性质，计算f, g C.对于有限集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 d_1, d_2, ..., d_h。他证明，如果 k <大于或等于> 4，q > 2k + 6，P(d_l) * P(d_m) 对于 l * m 和 SIGMA_l P(d_l) * 0，则 S 是唯一性范围集 他还给出了有限集的一些其他充分条件。是唯一性范围集。

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。

J.Noguchi: "Nevanlinna-Cartan theory over function fields and a Dio-phantine equation" J.reine angew.Math.489. 61-83 (1997)

J.Noguchi：“函数域的 Nevanlinna-Cartan 理论和 Diophantine 方程”J.reine angew.Math.489。