Algebraic cycles and intersections of three quadrics

TL;DR

This paper proves that smooth complete intersections of three quadrics with even dimension have a special Chow-K"unneth decomposition, leading to K3-like properties in their Chow rings, and extends this to double planes.

Contribution

It establishes a multiplicative Chow-K"unneth decomposition for such intersections and double planes, revealing new structural properties of their Chow rings.

Findings

Chow ring of powers of Y exhibits K3-like behaviour.

Existence of multiplicative Chow-K"unneth decomposition for Y.

Extension of decomposition results to double planes.

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-K\"unneth 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-K\"unneth decomposition for double planes.