Some new Fano varieties with a multiplicative Chow-Künneth decomposition

Abstract

Let $Y$ be a smooth dimensionally transverse intersection of the Grassmannian $Gr(2,n)$ with 3 Plücker hyperplanes. We show that $Y$ admits a multiplicative Chow-Künneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of the Chow ring of powers of $Y$ injects into cohomology.

arXiv comment16 pages, to appear in Osaka J. Math., comments welcome. arXiv admin note: substantial text overlap with arXiv:2009.11061; text overlap with arXiv:2107.10051, arXiv:2105.02016, arXiv:2105.02224, arXiv:2110.11791, arXiv:2108.08547

References in corpus (8)

• Determinantal hypersurfaces
• Projectors on the intermediate algebraic Jacobians
• On the Chow ring of Cynk-Hulek Calabi-Yau varieties and Schreieder varieties
• Motivic decompositions for the Hilbert scheme of points of a K3 surface
• On the Chow theory of projectivizations
• Algebraic cycles and Gushel-Mukai fivefolds
• Motives and the Pfaffian-Grassmannian equivalence
• Algebraic cycles and intersections of three quadrics