{"title":"Uniform rational polytopes of foliated threefolds and the global ACC","authors":"Jihao Liu, Fanjun Meng, Lingyao Xie","doi":"10.1112/jlms.12950","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we show the existence of uniform rational lc polytopes for foliations with functional boundaries in dimension <span></span><math>\n <semantics>\n <mrow>\n <mo>⩽</mo>\n <mn>3</mn>\n </mrow>\n <annotation>$\\leqslant 3$</annotation>\n </semantics></math>. As an application, we prove the global ACC for foliated threefolds with arbitrary DCC coefficients. We also provide applications on the accumulation points of lc thresholds of foliations in dimension <span></span><math>\n <semantics>\n <mrow>\n <mo>⩽</mo>\n <mn>3</mn>\n </mrow>\n <annotation>$\\leqslant 3$</annotation>\n </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"109 6","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12950","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we show the existence of uniform rational lc polytopes for foliations with functional boundaries in dimension . As an application, we prove the global ACC for foliated threefolds with arbitrary DCC coefficients. We also provide applications on the accumulation points of lc thresholds of foliations in dimension .
期刊介绍：
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
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