导曲线分担超平面的正规定则  

A Criterion of Normality That the Derived Curve Shares the Hyperplane

作　　者：王睿为 

机构地区：[1]上海理工大学理学院,上海

出　　处：《理论数学》2024年第6期341-350,共10页Pure Mathematics

摘　　要：本文利用正规族理论等相关知识,研究了导曲线分担处于一般位置的超平面的正规定则,得到了如下结果:设ℱ是一族从区域D⊂ℂ到ℙN(ℂ)的全纯曲线,Hl={x∈PN(C):〈x,αl〉=0}≠H0是ℙN(ℂ)中处于一般位置的超平面,其中αl=(αl0,αl1,⋯,αlN)T,l=1,2,⋯,2N+1,H0={x0=0}。如果对任意的f∈ℱ,满足:若∇f(z)∈Hl,则f(z)∈Hl;若f(z)∈∪l=12N+1Hl,那么|f(z),H0|||f(z)|⋅|H0||≥δ;若f(z)∈∪l=12N+1Hl,则|〈∇f(z),Hl〉||f0(z)|2≤1δ,其中0D上正规。In this paper, using the normal family theory and other relevant knowledge, we study a criterion of normality that the derived curve shares the hyperplane in the general position, and get the following result: letℱbe a family of holomorphic maps of a domainD⊂ℂtoℙN(ℂ). LetHl={x∈PN(C):〈x,αl〉=0}≠H0be hyperplanes inℙN(ℂ)located in general position, whereαl=(αl0,αl1,⋯,αlN)T,l=1,2,⋯,2N+1,H0={x0=0}. Assume the following conditions holdfor everyf∈ℱ: if∇f(z)∈Hl, thenf(z)∈Hl;iff(z)∈∪l=12N+1Hl, then|〈f(z),H0〉|||f(z)|⋅|H0||≥δ;iff(z)∈∪l=12N+1Hlthen|〈∇f(z),Hl〉||f0(z)|2≤1δ, where0D.

关 键 词：正规族 全纯曲线 分担超平面 导曲线 

分 类 号：G63[文化科学—教育学]