Algebraic cycles and intersections of a quadric and a cubic

Abstract

Abstract Let Y be a smooth complete intersection of a quadric and a cubic in ℙ n {\mathbb{P}^{n}} , with n 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 behavior. As a by-product of the argument, we also establish a multiplicative Chow–Künneth decomposition for the resolution of singularities of a general nodal cubic hypersurface of even dimension.