A cdh approach to zero-cycles on singular varieties

TL;DR

This paper explores the Chow group of zero-cycles on singular varieties using the cdh topology, establishing new comparisons with resolutions of singularities and extending known results to higher dimensions.

Contribution

It introduces cdh versions of zero-cycle groups and Albanese maps, and compares these with classical groups on resolutions, advancing understanding of zero-cycles on singular varieties.

Findings

Established comparisons between zero-cycle groups on singular varieties and their resolutions.

Extended known results on Chow groups of zero-cycles to higher-dimensional varieties.

Provided new insights into the structure of zero-cycles on singular algebraic varieties.

Abstract

We study the Chow group of zero-cycles on singular varieties using the cdh topology. We define the cdh versions of the zero-cycles and albanese maps. We prove results comparing these groups for a singular variety with the similar groups on the resolution of singularities. We use these to prove some results about the known Chow group of zero-cycles on surfaces and threefolds and some cases of arbitrary dimension.