{"title":"齐次Siegel域上Hartogs域间真全纯映射的分类","authors":"Lei Wang","doi":"10.1007/s10114-023-2278-4","DOIUrl":null,"url":null,"abstract":"<div><p>The Hartogs domain over homogeneous Siegel domain <i>D</i><sub><i>N,s</i></sub> (<i>s</i> > 0) is defined by the inequality ∥ζ∥<sup>2</sup> < <i>K</i><sub><i>D</i></sub>(<i>z, z</i>)<sup>−<i>s</i></sup>, where <i>D</i> is a homogeneous Siegel domain of type II, (<i>z, ζ</i>) ∈ <i>D</i> × ℂ<sup><i>N</i></sup> and <i>K</i><sub><i>D</i></sub>(<i>z, z</i>) is the Bergman kernel of <i>D</i>. Recently, Seo obtained the rigidity result that proper holomorphic mappings between two equidimensional domains <i>D</i><sub><i>N,s</i></sub> and <i>D′</i><sub><i>N′,s′</i></sub> are biholomorphisms for <i>N</i> ≥ 2. In this article, we find a counter-example to show that the rigidity result is not true for <i>D</i><sub>1,<i>s</i></sub> and obtain a classification of proper holomorphic mappings between <i>D</i><sub>1,<i>s</i></sub> and <i>D′</i><sub>1,<i>s′</i></sub>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Classification of Proper Holomorphic Mappings between Hartogs Domains over Homogeneous Siegel Domains\",\"authors\":\"Lei Wang\",\"doi\":\"10.1007/s10114-023-2278-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The Hartogs domain over homogeneous Siegel domain <i>D</i><sub><i>N,s</i></sub> (<i>s</i> > 0) is defined by the inequality ∥ζ∥<sup>2</sup> < <i>K</i><sub><i>D</i></sub>(<i>z, z</i>)<sup>−<i>s</i></sup>, where <i>D</i> is a homogeneous Siegel domain of type II, (<i>z, ζ</i>) ∈ <i>D</i> × ℂ<sup><i>N</i></sup> and <i>K</i><sub><i>D</i></sub>(<i>z, z</i>) is the Bergman kernel of <i>D</i>. Recently, Seo obtained the rigidity result that proper holomorphic mappings between two equidimensional domains <i>D</i><sub><i>N,s</i></sub> and <i>D′</i><sub><i>N′,s′</i></sub> are biholomorphisms for <i>N</i> ≥ 2. In this article, we find a counter-example to show that the rigidity result is not true for <i>D</i><sub>1,<i>s</i></sub> and obtain a classification of proper holomorphic mappings between <i>D</i><sub>1,<i>s</i></sub> and <i>D′</i><sub>1,<i>s′</i></sub>.</p></div>\",\"PeriodicalId\":50893,\"journal\":{\"name\":\"Acta Mathematica Sinica-English Series\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Sinica-English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10114-023-2278-4\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-023-2278-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
齐次Siegel域上的Hartogs域DN,s (s >0)由不等式∥ζ∥2 <定义;KD(z, z)−s,其中D是II型齐次Siegel域,(z, ζ)∈D × N, KD(z, z)是D的Bergman核。最近,Seo得到了两个等维域DN,s和D ' N ',s '之间的固有全纯映射在N≥2时是生物全纯的刚性结果。在本文中,我们找到一个反例来证明D1,s的刚性结果不成立,并得到D1,s与D ' 1,s '之间的真全纯映射的一个分类。
Classification of Proper Holomorphic Mappings between Hartogs Domains over Homogeneous Siegel Domains
The Hartogs domain over homogeneous Siegel domain DN,s (s > 0) is defined by the inequality ∥ζ∥2 < KD(z, z)−s, where D is a homogeneous Siegel domain of type II, (z, ζ) ∈ D × ℂN and KD(z, z) is the Bergman kernel of D. Recently, Seo obtained the rigidity result that proper holomorphic mappings between two equidimensional domains DN,s and D′N′,s′ are biholomorphisms for N ≥ 2. In this article, we find a counter-example to show that the rigidity result is not true for D1,s and obtain a classification of proper holomorphic mappings between D1,s and D′1,s′.
期刊介绍:
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.