Fulton, William; MacPherson, Robert A compactification of configuration spaces. (English) Zbl 0820.14037 Ann. Math. (2) 139, No. 1, 183-225 (1994). 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. Reviewer: E.Casas-Alvero (Barcelona) Cited in 15 ReviewsCited in 158 Documents 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 PDF BibTeX XML Cite \textit{W. Fulton} and \textit{R. MacPherson}, Ann. Math. (2) 139, No. 1, 183--225 (1994; Zbl 0820.14037) Full Text: DOI OpenURL