{"title":"全纯叶的可微等奇异性","authors":"Rogério Mol, R. Rosas","doi":"10.5427/JSING.2019.19F","DOIUrl":null,"url":null,"abstract":"We prove that a $C^{\\infty}$ equivalence between germs holomorphic foliations at $({\\mathbb C}^2,0)$ establishes a bijection between the sets of formal separatrices preserving equisingularity classes. As a consequence, if one of the foliations is of second type, so is the other and they are equisingular.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2016-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Differentiable equisingularity of holomorphic foliations\",\"authors\":\"Rogério Mol, R. Rosas\",\"doi\":\"10.5427/JSING.2019.19F\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that a $C^{\\\\infty}$ equivalence between germs holomorphic foliations at $({\\\\mathbb C}^2,0)$ establishes a bijection between the sets of formal separatrices preserving equisingularity classes. As a consequence, if one of the foliations is of second type, so is the other and they are equisingular.\",\"PeriodicalId\":44411,\"journal\":{\"name\":\"Journal of Singularities\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2016-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Singularities\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5427/JSING.2019.19F\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Singularities","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5427/JSING.2019.19F","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Differentiable equisingularity of holomorphic foliations
We prove that a $C^{\infty}$ equivalence between germs holomorphic foliations at $({\mathbb C}^2,0)$ establishes a bijection between the sets of formal separatrices preserving equisingularity classes. As a consequence, if one of the foliations is of second type, so is the other and they are equisingular.
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