{"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":null,"pages":null},"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}
引用次数: 0
Abstract
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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