{"title":"$\\ mathm {Gr}(3,6)$的余维2线性截面的动机","authors":"R. Laterveer","doi":"10.3836/tjm/1502179351","DOIUrl":null,"url":null,"abstract":"We consider Fano sevenfolds $Y$ obtained by intersecting the Grassmannian $\\mathrm{Gr}(3,6)$ with a codimension 2 linear subspace (with respect to the Pl\\\"ucker embedding). We prove that the motive of $Y$ is Kimura finite-dimensional. We also prove the generalized Hodge conjecture for all powers of $Y$.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Motive of Codimension 2 Linear Sections of $\\\\mathrm{Gr}(3,6)$\",\"authors\":\"R. Laterveer\",\"doi\":\"10.3836/tjm/1502179351\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider Fano sevenfolds $Y$ obtained by intersecting the Grassmannian $\\\\mathrm{Gr}(3,6)$ with a codimension 2 linear subspace (with respect to the Pl\\\\\\\"ucker embedding). We prove that the motive of $Y$ is Kimura finite-dimensional. We also prove the generalized Hodge conjecture for all powers of $Y$.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3836/tjm/1502179351\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3836/tjm/1502179351","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Motive of Codimension 2 Linear Sections of $\mathrm{Gr}(3,6)$
We consider Fano sevenfolds $Y$ obtained by intersecting the Grassmannian $\mathrm{Gr}(3,6)$ with a codimension 2 linear subspace (with respect to the Pl\"ucker embedding). We prove that the motive of $Y$ is Kimura finite-dimensional. We also prove the generalized Hodge conjecture for all powers of $Y$.
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