The homotopy type of the complement of the coordinate subspace arrangement

An arrangement = {L₁,…,L_r} in ℂⁿ is called coordinate if every L_i for i = 1,…,r is a coordinate subspace. We describe the unstable homotopy type of the complement U() := ℂ^m\⋃ _i=1 ^rL_i of a given coordinate subspace arrangement by combining the methods of classical homotopy theory and the new achievements of Toric Topology. As a corollary we obtain a new proof of the Golod result considering the rationality of the Poincaré series of certain local rings. (PDF file)