Li — Wonderful Compactifications Of Arrangements Of Subvarieties (2006)

We define the wonderful compactification of an arrangement of subvarieties. Given a complex nonsingular algebraic variety \(Y\) and certain collection \(\mathcal{ G}\) of subvarieties of \(Y\), the wonderful compactification \(Y_\mathcal{ G}\) can be constructed by a sequence of blow-ups of \(Y\) along the subvarieties of the arrangement. This generalizes the Fulton-MacPherson configuration spaces and the wonderful models given by De Concini and Procesi. We give a condition on the order of blow-ups in the construction of \(Y_\mathcal{ G}\) such that each blow-up is along a nonsingular center.