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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 thesubvarieties of the arrangement. This generalizes the Fulton-MacPhersonconfiguration 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.

Wonderful compactification of an arrangement of subvarieties