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A compactification of configuration spaces. (English) Zbl 0820.14037
The authors introduce and study a natural and very nice compactification X[n] of the configuration space F(X,n) of n distinct labeled points in a nonsingular algebraic variety X. X[n] is nonsingular and may be obtained from the cartesian product X n by a sequence of blow-ups. The locus of the degenerate configurations, X[n]-F(X,n), is a divisor with normal crossings whose components are explicitly described. Finally the intersection ring (rational cohomology ring in the complex case) of X[n] as well as those of the components of X[n]-F(X,n) and their intersections are computed.

14M99Special algebraic varieties
14N10Enumerative problems (algebraic geometry)
14C17Intersection theory, etc.