M.N. Boukhetouta, M. Krachni, F. Yazid, F.S. Djeradi
{"title":"HOLOMORPHIC EXTENSION","authors":"M.N. Boukhetouta, M. Krachni, F. Yazid, F.S. Djeradi","doi":"10.37418/amsj.12.1.14","DOIUrl":null,"url":null,"abstract":"In this paper, we prove that if there exists a holomorphic, proper, surjective map defined on a complex manifold $ X $ into a smooth algebraic curve with parallelizable fibers, then any holomorphic mappings defined on the Hartogs domain $ T $ of $\\mathbb{C}^n$ can be extended holomorphically (resp. meromorphically) from $ \\Delta ^n \\setminus Z $ into $ X $, where $ Z $ is an analytic subset of $\\Delta^n $ such that codimension of $ Z $ at least 2.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"46 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics: Scientific Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37418/amsj.12.1.14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we prove that if there exists a holomorphic, proper, surjective map defined on a complex manifold $ X $ into a smooth algebraic curve with parallelizable fibers, then any holomorphic mappings defined on the Hartogs domain $ T $ of $\mathbb{C}^n$ can be extended holomorphically (resp. meromorphically) from $ \Delta ^n \setminus Z $ into $ X $, where $ Z $ is an analytic subset of $\Delta^n $ such that codimension of $ Z $ at least 2.
在本文中,我们证明了如果存在一个定义在复流形$ X $上的全纯的、固有的满射映射到具有可并行纤维的光滑代数曲线上,那么定义在$\mathbb{C}^n$的Hartogs定域$ T $上的任何全纯映射都可以被全纯扩展。亚纯地)从$\Delta^n \set - Z $变成$ X $,其中$ Z $是$\Delta^n $的解析子集,使得$ Z $的余维至少为2。