$\ mathm {Gr}(3,6)$的余维2线性截面的动机

Pub Date : 2021-09-01 DOI:10.3836/tjm/1502179351
R. Laterveer
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引用次数: 0

摘要

我们考虑通过Grassmannian$\mathrm{Gr}(3,6)$与余维2线性子空间(关于Pl“ucker嵌入)相交得到的Fano七重$Y$。我们证明了$Y$的动机是Kimura有限维的。我们还证明了对$Y$所有幂的广义Hodge猜想。
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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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