Algebraic cycles and intersections of three quadrics

Abstract

Let $Y$ be a smooth complete intersection of three quadrics, and assume the dimension of $Y$ is even. We show that $Y$ has a multiplicative Chow-Künneth decomposition, in the sense of Shen-Vial. As a consequence, the Chow ring of (powers of) $Y$ displays K3-like behaviour. As a by-product of the argument, we also establish a multiplicative Chow-Künneth decomposition for double planes.

19 pages, to appear in Math. Proceedings of the Cambridge Philosophical Society, comments welcome. arXiv admin note: substantial text overlap with arXiv:2105.02224, arXiv:2105.02016, arXiv:2009.11061

References in corpus (2)

• The Derived Category of the Intersection of Four Quadrics
• Algebraic cycles and intersections of 2 quadrics

Cited by in corpus (2)

• On the tautological ring of Humbert curves
• Some new Fano varieties with a multiplicative Chow-Künneth decomposition