{"title":"立方超曲面上的直线","authors":"Jean-Louis Colliot-Th'elene","doi":"10.2140/akt.2018.3.723","DOIUrl":null,"url":null,"abstract":"Over any complex cubic hypersurface of dimension at least 2, the Chow group of 1-dimensional cycles is spanned by the lines lying on the hypersurface. The smooth case has already been given several other proofs. \n-- \nOn montre que sur toute hypersurface cubique complexe de dimension au moins 2, le groupe de Chow des cycles de dimension 1 est engendre par les droites. Le cas lisse est un theoreme connu. La demonstration ici donnee repose sur un resultat sur les surfaces geometriquement rationnelles sur un corps quelconque (1983), obtenu via la K-theorie algebrique.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2017-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/akt.2018.3.723","citationCount":"0","resultStr":"{\"title\":\"Droites sur les hypersurfaces cubiques\",\"authors\":\"Jean-Louis Colliot-Th'elene\",\"doi\":\"10.2140/akt.2018.3.723\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Over any complex cubic hypersurface of dimension at least 2, the Chow group of 1-dimensional cycles is spanned by the lines lying on the hypersurface. The smooth case has already been given several other proofs. \\n-- \\nOn montre que sur toute hypersurface cubique complexe de dimension au moins 2, le groupe de Chow des cycles de dimension 1 est engendre par les droites. Le cas lisse est un theoreme connu. La demonstration ici donnee repose sur un resultat sur les surfaces geometriquement rationnelles sur un corps quelconque (1983), obtenu via la K-theorie algebrique.\",\"PeriodicalId\":42182,\"journal\":{\"name\":\"Annals of K-Theory\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2017-03-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.2140/akt.2018.3.723\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/akt.2018.3.723\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of K-Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/akt.2018.3.723","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Over any complex cubic hypersurface of dimension at least 2, the Chow group of 1-dimensional cycles is spanned by the lines lying on the hypersurface. The smooth case has already been given several other proofs.
--
On montre que sur toute hypersurface cubique complexe de dimension au moins 2, le groupe de Chow des cycles de dimension 1 est engendre par les droites. Le cas lisse est un theoreme connu. La demonstration ici donnee repose sur un resultat sur les surfaces geometriquement rationnelles sur un corps quelconque (1983), obtenu via la K-theorie algebrique.
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