Algebraic cycles and intersections of a quadric and a cubic

Abstract

Let $Y$ be a smooth complete intersection of a quadric and a cubic in ${\mathbb{P}}^n$, 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 behaviour. 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.

arXiv comment14 pages, comments very welcome. arXiv admin note: substantial text overlap with arXiv:2105.02016; text overlap with arXiv:2009.11061