ИСТИНА

We describe the cohomology of the quotient Z_K/H of a moment-angle complex Z_K by a freely acting subtorus H in T^m by establishing a ring isomorphism of H*(Z_K/H,R) with an appropriate Tor-algebra of the face ring R[K], with coefficients in an arbitrary commutative ring R with unit. The quotients Z_K/H include moment-angle manifolds themselves, projective toric manifolds (the result was known for both these cases), and also `projective' moment-angle manifolds. The latter admit non-Kaehler complex-analytic structures as LVM-manifolds. We prove the collapse of the corresponding Eilenberg-Moore spectral sequence using the extended functoriality of Tor with respect to `strongly homotopy multiplicative' maps in the category DASH, following Gugenheim-May and Munkholm.