Algebraic cycles and triple K3 burgers

TL;DR

This paper studies special algebraic surfaces with a unique cohomological splitting related to K3 surfaces, demonstrating a similar decomposition at the level of Chow groups for certain families.

Contribution

It introduces a new class of surfaces with a cohomological splitting and establishes a Chow group decomposition for specific families, linking transcendental cohomology to Chow motives.

Findings

Cohomological splitting into three parts for certain surfaces.

Chow group splitting analogous to cohomological decomposition.

Identification of families where Chow motives reflect cohomological structure.

Abstract

We consider surfaces of geometric genus $3$ with the property that their transcendental cohomology splits into $3$ pieces, each piece coming from a $K3$ surface. For certain families of surfaces with this property, we can show there is a similar splitting on the level of Chow groups (and Chow motives).