{"title":"Simultaneous Uniformization and Algebraic Correspondences","authors":"Mahan Mj, Sabyasachi Mukherjee","doi":"arxiv-2409.10468","DOIUrl":null,"url":null,"abstract":"We prove a generalization of the Bers' simultaneous uniformization theorem in\nthe world of algebraic correspondences. More precisely, we construct algebraic\ncorrespondences that simultaneously uniformize a pair of non-homeomorphic genus\nzero orbifolds. We also present a complex-analytic realization of the\nTeichm\\\"uller space of a punctured sphere in the space of correspondences.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"202 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10468","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
We prove a generalization of the Bers' simultaneous uniformization theorem in
the world of algebraic correspondences. More precisely, we construct algebraic
correspondences that simultaneously uniformize a pair of non-homeomorphic genus
zero orbifolds. We also present a complex-analytic realization of the
Teichm\"uller space of a punctured sphere in the space of correspondences.
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