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Zbl 0820.14037
Fulton, William; MacPherson, Robert
A compactification of configuration spaces. (English)
[J] Ann. Math. (2) 139, No.1, 183-225 (1994). ISSN 0003-486X; ISSN 1939-8980/e

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 $X\sp n$ 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.
[E.Casas-Alvero (Barcelona)]

MSC 2000:: *14M99 Special varieties
14N10 Enumerative problems (classical algebraic geometry)
14C17 Intersection theory

Keywords: compactification; configuration space; intersection ring

Cited in: Zbl 1238.14016 Zbl 1188.14003 Zbl 1187.14060 Zbl 1184.57023 Zbl 1050.14051 Zbl 1018.57015 Zbl 1053.81071 Zbl 0972.18005 Zbl 0992.14019 Zbl 0952.14032 Zbl 0980.55011 Zbl 0881.14004 Zbl 0871.14022 Zbl 0829.55008

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