The Degree of Proper Holomorphic MappingsBetween Special Domains in C^n  

作　　者：Jia Fu NING Xiang Yu ZHOU 

机构地区：[1]Department of Mathematics,Central South University,Changsha 410083,P.R.China [2]Institute of Mathematics,Academy of Mathematics and Systems Science,and Hua Loo-Keng Key Laboratory of Mathematics,Chinese Academy of Sciences,Beijing 100190,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2020年第4期395-400,共6页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11801572,11688101)。

摘　　要：Let Gi be closed Lie groups of U (n), Ω i be bounded Gi-invariant domains in C^n which contains 0, and O(C^n)^Gi = C, for i = 1, 2. It is known that if f : Ω 1 → Ω 2 is a proper holomorphic mapping, and f^-1{0} = {0}, then f is a polynomial mapping. In this paper, we provide an upper bound for the degree of such a polynomial mapping using the multiplicity of f .

关 键 词：Group action degree of polynomial mapping proper lomorphic mapping Bergman kernel invariant domain 

分 类 号：O174.14[理学—数学]