Geodesic
Spaces of geometrically generic configurations
Journal of the European Mathematical Society, Tome 10 (2008) no. 3, pp. 601-624 Cet article a éte moissonné depuis la source EMS Press

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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 
@article{JEMS_2008_10_3_a1,
     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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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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