A generalization of Sankaran and LVMB manifolds

In this paper we describe the construction of a new class of non-K"ahler compact complex manifolds. They can be seen as a generalization of Sankaran, OT and LVMB manifolds. Moreover, we give properties of these new spaces. Their Kodaira dimension is $-\mathrm{\infty }$ and under a mild condition they have algebraic dimension equal to zero.