{"title":"On Finite Parts of Divergent Complex Geometric Integrals and Their Dependence on a Choice of Hermitian Metric","authors":"Ludvig Svensson","doi":"10.1007/s12220-024-01773-9","DOIUrl":null,"url":null,"abstract":"<p>Let <i>X</i> be a reduced complex space of pure dimension. We consider divergent integrals of certain forms on <i>X</i> that are singular along a subvariety defined by the zero set of a holomorphic section of some holomorphic vector bundle <span>\\(E \\rightarrow X\\)</span>. Given a choice of Hermitian metric on <i>E</i> we define a finite part of the divergent integral. Our main result is an explicit formula for the dependence on the choice of metric of the finite part.\n</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Geometric Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12220-024-01773-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Let X be a reduced complex space of pure dimension. We consider divergent integrals of certain forms on X that are singular along a subvariety defined by the zero set of a holomorphic section of some holomorphic vector bundle \(E \rightarrow X\). Given a choice of Hermitian metric on E we define a finite part of the divergent integral. Our main result is an explicit formula for the dependence on the choice of metric of the finite part.
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