{"title":"具有规定分支数据的曲面上复杂投影结构的完整性","authors":"Thomas Le Fils","doi":"10.1112/topo.12287","DOIUrl":null,"url":null,"abstract":"<p>We characterize the representations of the fundamental group of a closed surface to <math>\n <semantics>\n <mrow>\n <msub>\n <mi>PSL</mi>\n <mn>2</mn>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>C</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$\\mathrm{PSL}_2(\\mathbb {C})$</annotation>\n </semantics></math> that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the holonomies of the spherical metrics with prescribed integral conical angles and the holonomies of affine structures with fixed conical angles on closed surfaces.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12287","citationCount":"0","resultStr":"{\"title\":\"Holonomy of complex projective structures on surfaces with prescribed branch data\",\"authors\":\"Thomas Le Fils\",\"doi\":\"10.1112/topo.12287\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We characterize the representations of the fundamental group of a closed surface to <math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mi>PSL</mi>\\n <mn>2</mn>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <mi>C</mi>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$\\\\mathrm{PSL}_2(\\\\mathbb {C})$</annotation>\\n </semantics></math> that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the holonomies of the spherical metrics with prescribed integral conical angles and the holonomies of affine structures with fixed conical angles on closed surfaces.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-03-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12287\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12287\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12287","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Holonomy of complex projective structures on surfaces with prescribed branch data
We characterize the representations of the fundamental group of a closed surface to that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the holonomies of the spherical metrics with prescribed integral conical angles and the holonomies of affine structures with fixed conical angles on closed surfaces.
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