In geometry, the Fulton–MacPherson compactification of the configuration space of n distinct labeled points in a compact complex manifold is a compact complex manifold that contains the configuration space as an open dense subset and is constructed in a canonical way. The notion was introduced by Fulton & MacPherson (1994).
References
Lecture 13: the Fulton–MacPherson compactification by A. Voronov. Fulton, W.; MacPherson, R. (1994). "Compactification of configuration spaces". Annals of Mathematics. 139: 183–225.