{"title":"代数循环与Verra四重","authors":"R. Laterveer","doi":"10.2748/tmj/1601085625","DOIUrl":null,"url":null,"abstract":"This note is about the Chow ring of Verra fourfolds. For a general Verra fourfold, we show that the Chow group of homologically trivial $1$-cycles is generated by conics. We also show that Verra fourfolds admit a multiplicative Chow-K\\\"unneth decomposition, and draw some consequences for the intersection product in the Chow ring of Verra fourfolds.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2019-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":"{\"title\":\"Algebraic cycles and Verra fourfolds\",\"authors\":\"R. Laterveer\",\"doi\":\"10.2748/tmj/1601085625\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This note is about the Chow ring of Verra fourfolds. For a general Verra fourfold, we show that the Chow group of homologically trivial $1$-cycles is generated by conics. We also show that Verra fourfolds admit a multiplicative Chow-K\\\\\\\"unneth decomposition, and draw some consequences for the intersection product in the Chow ring of Verra fourfolds.\",\"PeriodicalId\":54427,\"journal\":{\"name\":\"Tohoku Mathematical Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2019-06-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tohoku Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2748/tmj/1601085625\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tohoku Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2748/tmj/1601085625","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
This note is about the Chow ring of Verra fourfolds. For a general Verra fourfold, we show that the Chow group of homologically trivial $1$-cycles is generated by conics. We also show that Verra fourfolds admit a multiplicative Chow-K\"unneth decomposition, and draw some consequences for the intersection product in the Chow ring of Verra fourfolds.