On the Motive of Codimension 2 Linear Sections of Gr(3, 6)

Robert Laterveer

doi:10.3836/tjm/1502179351

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 Plücker 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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Robert Laterveer. "On the Motive of Codimension 2 Linear Sections of $\mathrm{Gr}(3,6)$ ." Tokyo J. Math. 45 (1) 89 - 101, June 2022. https://doi.org/10.3836/tjm/1502179351

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Received: 13 July 2020; Revised: 8 January 2021; Published: June 2022

First available in Project Euclid: 4 October 2021

MathSciNet: MR4484253

zbMATH: 1503.14008

Digital Object Identifier: 10.3836/tjm/1502179351

Subjects:

Primary: 14C15

Secondary: 14C25 , 14C30

Keywords: algebraic cycles , Bloch-Beilinson conjectures , Chow groups , generalized Hodge conjecture , Kimura finite-dimensionality , motives

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