The Chow ring of a wonderful compactification

Abstract

The theory of wonderful compactifications provides a common framework encompassing the constructions of important varieties such as the Fulton-MacPherson configuration spaces, the moduli space of $n$-pointed stable rational curves, and the De Concini-Procesi models of subspace arrangements, and, more generally, of smooth compactifications in which the subvarieties in a building set are replaced by a simple normal crossings boundary divisor. We give a presentation of the Chow ring of a wonderful compactification, assuming only that the Chow ring of the ambient variety surjects onto that of each subvariety in the induced arrangement. Our results recover and extend many previously known presentations and apply to a broad range of new examples.