{"title":"Notes on the Hodge conjecture for Fermat varieties","authors":"Genival da Silva","doi":"10.1017/exp.2021.14","DOIUrl":null,"url":null,"abstract":"Abstract We review a combinatoric approach to the Hodge conjecture for Fermat varieties and announce new cases where the conjecture is true. We show the Hodge conjecture for Fermat fourfolds $ {X}_m^4 $ of degree m ≤ 100 coprime to 6, and also prove the conjecture for $ {X}_{21}^n $ and $ {X}_{27}^n $, for all n.","PeriodicalId":12269,"journal":{"name":"Experimental Results","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Experimental Results","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/exp.2021.14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract We review a combinatoric approach to the Hodge conjecture for Fermat varieties and announce new cases where the conjecture is true. We show the Hodge conjecture for Fermat fourfolds $ {X}_m^4 $ of degree m ≤ 100 coprime to 6, and also prove the conjecture for $ {X}_{21}^n $ and $ {X}_{27}^n $, for all n.
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