Torus actions, equivariant moment-angle complexes, and coordinate subspace arrangements.

We show that the cohomology algebra of the complement of a coordinate subspace arrangement in $m$-dimensional complex space is isomorphic to the cohomology algebra of Stanley–Reisner face ring of a certain simplicial complex on $m$ vertices. Then we calculate the latter cohomology algebra by means of the standard Koszul resolution of polynomial ring. To prove these facts we construct an equivariant with respect to the torus action homotopy equivalence between the complement of a coordinate subspace arrangement and the moment-angle complex defined by the simplicial complex, then investigate the equivariant topology of the moment-angle complex and apply the Eilenberg–Moore spectral sequence.