  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. (The face ring is regarded as a module over the polynomial ring
on m generators.) 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. The moment-angle
complex is a certain subset of a unit poly-disk in m-dimensional complex space
invariant with respect to the action of an m-dimensional torus. This complex is
a smooth manifold provided that the simplicial complex is a simplicial sphere,
but otherwise has more complicated structure. Then we investigate the
equivariant topology of the moment-angle complex and apply the Eilenberg-Moore
spectral sequence. We also relate our results with well known facts in the
theory of toric varieties and symplectic geometry.
