{"title":"LELONG NUMBERS OF <i>m</i>-SUBHARMONIC FUNCTIONS ALONG SUBMANIFOLDS","authors":"Jianchun Chu, Nicholas McCleerey","doi":"10.1017/s1474748023000385","DOIUrl":null,"url":null,"abstract":"Abstract We study the possible singularities of an m -subharmonic function $\\varphi $ along a complex submanifold V of a compact Kähler manifold, finding a maximal rate of growth for $\\varphi $ which depends only on m and k , the codimension of V . When $k < m$ , we show that $\\varphi $ has at worst log poles along V , and that the strength of these poles is moreover constant along V . This can be thought of as an analogue of Siu’s theorem.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"103 7","pages":"0"},"PeriodicalIF":1.1000,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Institute of Mathematics of Jussieu","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s1474748023000385","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract We study the possible singularities of an m -subharmonic function $\varphi $ along a complex submanifold V of a compact Kähler manifold, finding a maximal rate of growth for $\varphi $ which depends only on m and k , the codimension of V . When $k < m$ , we show that $\varphi $ has at worst log poles along V , and that the strength of these poles is moreover constant along V . This can be thought of as an analogue of Siu’s theorem.
期刊介绍：
The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.
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