{"title":"Uniform $L^2$-estimates for flat nontrivial line bundles on compact complex manifolds","authors":"Yoshinori Hashimoto, Takayuki Koike, Shin-ichi Matsumura","doi":"arxiv-2409.05300","DOIUrl":null,"url":null,"abstract":"In this paper, we extend the uniform $L^2$-estimate of\n$\\bar{\\partial}$-equations for flat nontrivial line bundles, proved for compact\nK\\\"ahler manifolds in the previous work, to compact complex manifolds. In the\nproof, by tracing the Dolbeault isomorphism in detail, we derive the desired\n$L^2$-estimate directly from Ueda's lemma.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"29 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","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-2409.05300","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 extend the uniform $L^2$-estimate of
$\bar{\partial}$-equations for flat nontrivial line bundles, proved for compact
K\"ahler manifolds in the previous work, to compact complex manifolds. In the
proof, by tracing the Dolbeault isomorphism in detail, we derive the desired
$L^2$-estimate directly from Ueda's lemma.