{"title":"论有理曲线邻域上的分形函数场","authors":"Serge Lvovski","doi":"arxiv-2408.14061","DOIUrl":null,"url":null,"abstract":"Suppose that $F$ is a smooth and connected complex surface (not necessarily\ncompact) containing a smooth rational curve with positive self-intersection. We\nprove that if there exists a non-constant meromorphic function on $F$, then the\nfield of meromorphic functions on $F$ is isomorphic to the field of rational\nfunctions in one or two variables over $\\mathbb C$.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"41 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On fields of meromorphic functions on neighborhoods of rational curves\",\"authors\":\"Serge Lvovski\",\"doi\":\"arxiv-2408.14061\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Suppose that $F$ is a smooth and connected complex surface (not necessarily\\ncompact) containing a smooth rational curve with positive self-intersection. We\\nprove that if there exists a non-constant meromorphic function on $F$, then the\\nfield of meromorphic functions on $F$ is isomorphic to the field of rational\\nfunctions in one or two variables over $\\\\mathbb C$.\",\"PeriodicalId\":501142,\"journal\":{\"name\":\"arXiv - MATH - Complex Variables\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-26\",\"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-2408.14061\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.14061","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On fields of meromorphic functions on neighborhoods of rational curves
Suppose that $F$ is a smooth and connected complex surface (not necessarily
compact) containing a smooth rational curve with positive self-intersection. We
prove that if there exists a non-constant meromorphic function on $F$, then the
field of meromorphic functions on $F$ is isomorphic to the field of rational
functions in one or two variables over $\mathbb C$.