On the motive of codimension 2 linear sections of $Gr(3,6)$

Abstract

We consider Fano sevenfolds $Y$ obtained by intersecting the Grassmannian $Gr(3,6)$ 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 $Y$.

11 pages, to appear in Tokyo J. Math., comments welcome. arXiv admin note: text overlap with arXiv:2009.11061, arXiv:2105.03171

References in corpus (4)

• Homological projective duality for Grassmannians of lines
• The generalized Franchetta conjecture for some hyper-Kähler varieties, II
• The generalized Hodge and Bloch conjectures are equivalent for general complete intersections, II
• On the Chow theory of projectivizations