Algebraic cycles and intersections of a quadric and a cubic.

Let Y be a smooth complete intersection of a quadric and a cubic in ℙn, 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. [ABSTRACT FROM AUTHOR]