Geodesic
Spaces of geometrically generic configurations
Journal of the European Mathematical Society, Tome 10 (2008) no. 3, pp. 601-624

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DOI

Let X denote either CPm or Cm. We study certain analytic properties of the space En(X,gp) of ordered geometrically generic n-point configurations in X. This space consists of all q=(q1​,...,qn​)∈Xn such that no m+1 of the points q1​,...,qn​ belong to a hyperplane in X. In particular, we show that for a big enough n any holomorphic map f:En(CPm,gp)→En(CPm,gp) commuting with the natural action of the symmetric group S(n) in En(CPm,gp) is of the form f(q)=τ(q)q=(τ(q)q1​,...,τ(q)qn​), q∈En(CPm,gp), where τ:En(CPm,gp)→PSL(m+1,C) is an S(n)-invariant holomorphic map. A similar result holds true for mappings of the configuration space En(Cm,gp).
DOI : 10.4171/jems/124
Classification : 14-XX, 32-XX, 00-XX
Keywords: Configuration space, geometrically generic configurations, vector braids, points in general position, holomorphic endomorphism 
Yoel Feler. Spaces of geometrically generic configurations. Journal of the European Mathematical Society, Tome 10 (2008) no. 3, pp. 601-624. doi: 10.4171/jems/124
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     author = {Yoel Feler},
     title = {Spaces of geometrically generic configurations},
     journal = {Journal of the European Mathematical Society},
     pages = {601--624},
     year = {2008},
     volume = {10},
     number = {3},
     doi = {10.4171/jems/124},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/124/}
}
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