LVMB manifolds and quotients of toric varieties

In this article, we study a class of manifolds introduced by Bosio called $\text{LVMB}$ manifolds. We provide an interpretation of his construction in terms of quotient of toric manifolds by complex Lie groups. Furthermore, $\text{LVMB}$ manifolds extend a class of manifolds obtained by Meersseman, called $\text{LVM}$ manifolds, and we give a characterization of these manifolds using our toric description. Finally, we give an answer to a question asked by Cupit-Foutou and Zaffran.