Geodesic
Configuration spaces of $n$ lines in affine $(n+k)$-space
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 5, pp. 33-45
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In this paper, we study the space of configurations of $n$ lines in the affine space of dimension $n+k$. We give a topological description of these spaces in terms of some fiber spaces and describe more specifically some interesting cases. 
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M. Boege; L. Montejano. Configuration spaces of $n$ lines in affine $(n+k)$-space. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 5, pp. 33-45. http://geodesic.mathdoc.fr/item/FPM_2005_11_5_a2/

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