## 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.

### MSC:

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

### Keywords:

compactification; configuration space; intersection ring
Full Text: