Algebraic cycles and Gushel-Mukai fivefolds

Abstract

We show that Gushel-Mukai fivefolds admit 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 these varieties injects into cohomology.

19 pages, to appear in J. Pure and Applied Algebra, comments welcome. v2: minor corrections to the proof of Corollary 4.1

References in corpus (3)

• On the splitting of the Bloch-Beilinson filtration
• The generalized Hodge and Bloch conjectures are equivalent for general complete intersections, II
• On the Chow groups of Plücker hypersurfaces in Grassmannians

Cited by in corpus (6)

• Algebraic cycles and intersections of 2 quadrics
• On the Chow ring of Fano varieties on the Fatighenti-Mongardi list
• On the tautological ring of Humbert curves
• Algebraic cycles on Gushel-Mukai varieties
• Chow groups of Gushel-Mukai fivefolds
• Some new Fano varieties with a multiplicative Chow-Künneth decomposition