The authors introduce and study a natural and very nice compactification
of the configuration space
distinct labeled points in a nonsingular algebraic variety
is nonsingular and may be obtained from the cartesian product
by a sequence of blow-ups. The locus of the degenerate configurations,
, is a divisor with normal crossings whose components are explicitly described. Finally the intersection ring (rational cohomology ring in the complex case) of
as well as those of the components of
and their intersections are computed.