The Degree of Proper Holomorphic Mappings Between Special Domains in ℂn

被引：0
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作者：
Jia Fu Ning
Xiang Yu Zhou
机构：
[1] Central South University,Department of Mathematics
[2] Chinese Academy of Sciences,Institute of Mathematics, Academy of Mathematics and Systems Science, and Hua Loo
来源：
Acta Mathematica Sinica, English Series | 2020年 / 36卷
关键词：
Group action; degree of polynomial mapping; proper lomorphic mapping; Bergman kernel; invariant domain; 32H35; 32M05; 32A07;
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学科分类号：
摘要：
Let Gi be closed Lie groups of U(n), Ωi be bounded Gi-invariant domains in ℂn which contains 0, and O(ℂn)Gi = ℂ, for i = 1, 2. It is known that if f: Ω1 →} Ω2 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：5
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