Wonderful compactification of an arrangement of subvarieties

Abstract

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.

30 pages, presentation is improved, to appear in the Michigan Mathematical Journal

References in corpus (1)

• Integral Expressions for the Vassiliev Knot Invariants