{"title":"论理性连接的内涵","authors":"C. Voisin","doi":"10.2140/gt.2022.26.2731","DOIUrl":null,"url":null,"abstract":"We prove that the integral cohomology modulo torsion of a rationally connected threefold comes from the integral cohomology of a smooth curve via the cylinder homomorphism associated to a family of $1$-cycles. Equivalently, it is of strong coniveau 1 in the sense of Benoist-Ottem.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"On the coniveau of rationally connected threefolds\",\"authors\":\"C. Voisin\",\"doi\":\"10.2140/gt.2022.26.2731\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the integral cohomology modulo torsion of a rationally connected threefold comes from the integral cohomology of a smooth curve via the cylinder homomorphism associated to a family of $1$-cycles. Equivalently, it is of strong coniveau 1 in the sense of Benoist-Ottem.\",\"PeriodicalId\":254292,\"journal\":{\"name\":\"Geometry & Topology\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-10-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometry & Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/gt.2022.26.2731\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry & Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/gt.2022.26.2731","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the coniveau of rationally connected threefolds
We prove that the integral cohomology modulo torsion of a rationally connected threefold comes from the integral cohomology of a smooth curve via the cylinder homomorphism associated to a family of $1$-cycles. Equivalently, it is of strong coniveau 1 in the sense of Benoist-Ottem.
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