On the Chow groups of Plücker hypersurfaces in Grassmannians

Abstract

Motivated by the generalized Bloch conjecture, we formulate a conjecture about the Chow groups of Plücker hypersurfaces in Grassmannians. We prove weak versions of this conjecture.

On the motive of codimension 2 linear sections of $\hbox{Gr}(3,6)$

“…Let Gr (3,6) be the Grassmannian of 3-dimensional linear subspaces of a fixed 6-dimensional vector space. In this note, we consider smooth complete intersections Y = Gr (3,6) ∩ H 1 ∩ H 2 ⊂ P 19 of the Grassmannian with 2 Plücker hyperplanes H 1 , H 2 . This Y is a 7-dimensional Fano variety of Hodge coniveau 3 (i.e.…”