{"title":"On holomorphic $\\mathbb{C}^*$-actions","authors":"Víctor León, Bruno Scárdua","doi":"arxiv-2408.09625","DOIUrl":null,"url":null,"abstract":"In this paper we study holomorphic actions of the complex multiplicative\ngroup on complex manifolds around a singular (fixed) point. We prove\nlinearization results for the germ of action and also for the whole action\nunder some conditions on the manifold. This can be seen as a follow-up to\nprevious works of M. Suzuki and other authors.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.09625","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 study holomorphic actions of the complex multiplicative
group on complex manifolds around a singular (fixed) point. We prove
linearization results for the germ of action and also for the whole action
under some conditions on the manifold. This can be seen as a follow-up to
previous works of M. Suzuki and other authors.