The Degree of Proper Holomorphic Mappings Between Special Domains in DOUBLE-STRUCK CAPITAL Cn

被引：0
|
作者：
Ning, Jia Fu [1 ]
Zhou, Xiang Yu [2 ,3 ]
机构：
[1] Cent South Univ, Dept Math, Changsha 410083, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
[3] Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2020年 / 36卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Group action; degree of polynomial mapping; proper lomorphic mapping; Bergman kernel; invariant domain; AUTOMORPHISMS;
D O I：
10.1007/s10114-020-9299-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let Gi be closed Lie groups of U(n), omega(i) be bounded G(i)-invariant domains in DOUBLE-STRUCK CAPITAL C-n which contains 0, and O(DOUBLE-STRUCK CAPITAL C-n)(Gi) = DOUBLE-STRUCK CAPITAL C, for i = 1, 2. It is known that if f: omega(1) ->} omega(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.
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页码：395 / 400
页数：6
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