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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.

14M99 Special varieties
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
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