{"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":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tokyo Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3836/tjm/1502179351","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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 $Y$.
期刊介绍：
The Tokyo Journal of Mathematics was founded in 1978 with the financial support of six institutions in the Tokyo area: Gakushuin University, Keio University, Sophia University, Tokyo Metropolitan University, Tsuda College, and Waseda University. In 2000 Chuo University and Meiji University, in 2005 Tokai University, and in 2013 Tokyo University of Science, joined as supporting institutions.
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