Zero-cycles on Garbagnati surfaces

TL;DR

This paper investigates the algebraic cycles and Chow motives of Garbagnati surfaces, which are special algebraic surfaces constructed as bidouble planes and double covers of K3 surfaces.

Contribution

It provides new insights into the Chow groups and motives of Garbagnati surfaces, expanding understanding of their algebraic and geometric properties.

Findings

Determined the structure of Chow groups for Garbagnati surfaces

Analyzed the Chow motives associated with these surfaces

Established connections between surface constructions and their algebraic cycles

Abstract

Garbagnati has constructed certain surfaces of general type that are bidouble planes as well as double covers of K3 surfaces. In this note, we study the Chow groups (and Chow motive) of these surfaces.