The Chow ring of relative Fulton-MacPherson space

TL;DR

This paper provides an explicit description of the Chow rings and Chow motives of configuration spaces of points in a nonsingular variety, constructed via wonderful compactification, extending understanding of their algebraic structure.

Contribution

It offers a detailed presentation of Chow rings and motives for configuration spaces of points in a nonsingular variety with a subvariety, using the wonderful compactification method.

Findings

Explicit Chow ring presentations for configuration spaces

Chow motives characterized for these spaces

Extension of previous constructions to algebraic invariants

Abstract

Suppose that X is a nonsingular variety and D is a nonsingular proper subvariety. Configuration spaces of distinct and non-distinct n points in X away from D were constructed by the author and B. Kim in arXiv:0806.3819, by using the method of wonderful compactification. In this paper, we give an explicit presentation of Chow motives and Chow rings of these configuration spaces.