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

Voir la notice de l'article provenant de la source EMS Press

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 
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     author = {Yoel Feler},
     title = {Spaces of geometrically generic configurations},
     journal = {Journal of the European Mathematical Society},
     pages = {601--624},
     publisher = {mathdoc},
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     year = {2008},
     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. http://geodesic.mathdoc.fr/articles/10.4171/jems/124/

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