{"title":"复数空间的非阿基米德理论和 cscK 问题","authors":"Pietro Mesquita-Piccione","doi":"arxiv-2409.06221","DOIUrl":null,"url":null,"abstract":"In this paper we develop an analogue of the Berkovich analytification for\nnon-necessarily algebraic complex spaces. We apply this theory to generalize to\narbitrary compact K\\\"ahler manifolds a result of Chi Li, proving that a\nstronger version of K-stability implies the existence of a unique constant\nscalar curvature K\\\"ahler metric.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A non-Archimedean theory of complex spaces and the cscK problem\",\"authors\":\"Pietro Mesquita-Piccione\",\"doi\":\"arxiv-2409.06221\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we develop an analogue of the Berkovich analytification for\\nnon-necessarily algebraic complex spaces. We apply this theory to generalize to\\narbitrary compact K\\\\\\\"ahler manifolds a result of Chi Li, proving that a\\nstronger version of K-stability implies the existence of a unique constant\\nscalar curvature K\\\\\\\"ahler metric.\",\"PeriodicalId\":501113,\"journal\":{\"name\":\"arXiv - MATH - Differential Geometry\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Differential Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06221\",\"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 - Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06221","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A non-Archimedean theory of complex spaces and the cscK problem
In this paper we develop an analogue of the Berkovich analytification for
non-necessarily algebraic complex spaces. We apply this theory to generalize to
arbitrary compact K\"ahler manifolds a result of Chi Li, proving that a
stronger version of K-stability implies the existence of a unique constant
scalar curvature K\"ahler metric.
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