{"title":"Local algebraicity and localization of the Bergman kernel on Stein spaces with finite type boundaries","authors":"Peter Ebenfelt, Soumya Ganguly, Ming Xiao","doi":"arxiv-2408.13989","DOIUrl":null,"url":null,"abstract":"On a two dimensional Stein space with isolated, normal singularities, smooth\nfinite type boundary, and locally algebraic Bergman kernel, we establish an\nestimate on the type of the boundary in terms of the local algebraic degree of\nthe Bergman kernel. As an application, we characterize two dimensional ball\nquotients as the only Stein spaces with smooth finite type boundary and locally\nrational Bergman kernel. A key ingredient in the proof of the degree estimate\nis a new localization result for the Bergman kernel of a pseudoconvex, finite\ntype domain in a complex manifold.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"59 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-2408.13989","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
On a two dimensional Stein space with isolated, normal singularities, smooth
finite type boundary, and locally algebraic Bergman kernel, we establish an
estimate on the type of the boundary in terms of the local algebraic degree of
the Bergman kernel. As an application, we characterize two dimensional ball
quotients as the only Stein spaces with smooth finite type boundary and locally
rational Bergman kernel. A key ingredient in the proof of the degree estimate
is a new localization result for the Bergman kernel of a pseudoconvex, finite
type domain in a complex manifold.